Probability

Problem 1101

A home pregnancy test's results show: 52 positive, 7 negative for pregnant; 9 positive, 72 negative for not pregnant. Find:
a. P(Positive | Pregnant) = $b. P(Pregnant | Positive) =$ c. P(Negative | Pregnant) = $d. P(Not Pregnant | Negative) =$

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Problem 1102

What is the term for patients feeling better after a sugar pill for headaches? A. randomization B. control C. experimental D. placebo.

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Problem 1103

$\vee 1$ 12 3 4 5 6 $\checkmark 7$ 78
If $P(A)=0.51, P(B)=0.6$ , and $P(A$ and $B)=0.41$ , find $P(A$ or $B)$ . $P(A \text { or } B)=$ $\square$ $\square$

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Problem 1104

Consider the following binomial probability distribution expression below. The number of trials, the number of successes, the probability of success and the probability of failure respectively are: $\binom{12}{7}(0.1)^{7}(0.9)^{5}$ $7,0.1,0.9,12$ $12,7,0.1,0.9$ $12,7,0.9,0.1$ $7,0.9,12,0.1$

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Problem 1105

(1 point) Below is a certain probability model: \begin{tabular}{|c|c|c|c|c|c|} \hline Outcome & $a$ & $b$ & $c$ & $d$ & $e$ \\ \hline Probability & 0.2 & & 0.15 & 0.05 & 0.3 \\ \hline \end{tabular}
Events $F$ and $G$ are given by $F=\{a, c, e\}, \quad G=\{b, c, e\} .$
Calculate each probability: $\begin{array}{l} P(b)=0.15 \\ P(F \cup G)=0.7 \\ P(F \cap G)=0.35 \\ P\left(F^{\prime}\right)=0.45 \end{array}$

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Problem 1106

In the game of roulette, a wheel consists of 38 slots numbered $0,00,1,2, \ldots, 36$ . To play the game, a metal ball is spun around the wheel and is allowed to fall into one of the numbered slots. If the number of the slot the ball falls into matches the number you selected, you win $\$ 35$ ; otherwise you lose $\$ 1$ . Complete parts (a) through ( g ) below. Click here to view the standard normal distribution table (page 1): Click here to view the standard normal distribution table (page 2). (a) Construct a probability distribution for the random variable $X$ , the winnings of each spin. (Type integers or decimals rounded to four decimal places as needed.)

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Problem 1107

4. A study of the weights of the brains of Swedish men varies according to a distribution that is approximately Normal with mean 1400 grams and standard deviation 20 grams.
If two Swedish men named Nordal and Hector are selected, what is the probability that Nordal's brain weighs at least 15 grams more than Hector's? (For full credit, show ALL work, including making a picture).

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Problem 1108

The life of a Radio Shack record player is normally distributed with a mean of 3.3 years and a standard deviation of 0.8 years. Radio Shack guarantees its record players for 2 years.
Find the probability that a record player will break down during the guarantee period. 0.03417 0.05208 0.06302 0.04218 0.03796 0.05729 0.04687

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Problem 1109

Out of 160 workers surveyed at a company, 37 walk to work. a. What is the experimental probability that a randomly selected worker at that company walks to work? b. Predict about how many of the 4000 workers at the company walk to work. a. The experimental probability is $\square$

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Problem 1110

According to a survey in a country, $39 \%$ of adults do not own a credit card. Suppose a simple random sample of 400 adults is obtained. Comple $\qquad$ B. Not normal because $\mathrm{n} \leq 0.05 \mathrm{~N}$ and $\mathrm{np}(1-\mathrm{p})<10$ C. Not normal because $n \leq 0.05 \mathrm{~N}$ and $\mathrm{np}(1-\mathrm{p}) \geq 10$ D. Approximately normal because $n \leq 0.05 \mathrm{~N}$ and $\mathrm{np}(1-\mathrm{p}) \geq 10$
Determine the mean of $\tilde{n}$ e sampling distribution of $\hat{p}$ . $\mu_{\hat{p}}=.39$ (Round to two decimal places as needed.) Determine the standard deviation of the sampling distribution of $\hat{p}$ . $\sigma_{\hat{p}}=.024$ (Round to three decimal places as needed.) (b) What is the probability that in a random sample of 400 adults, more than $42 \%$ do not own a credit card?
The probability is .1056 . (Round to four decimal places as needed.) Interpret this probability. If 100 different random samples of 400 adults were obtained, one would expect 11 to result in more than $42 \%$ not owning a credit card. (Round to the nearest integer as needed.) (c) What is the probability that in a random sample of 400 adults, between $34 \%$ and $42 \%$ do not own a credit card?
The probability is $\square$ (Round to four decimal places as needed.)

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Problem 1111

A student council has 15 members, including Yuko, Luigi, and Justip a) The staff advisor will select three members at random to be treasurer, secretary, and liaison to the principal. Determine the probability that the staff advisor will select Yuko to be treasurer, Luigi to be secretary, and Justin to be liaison.

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Problem 1112

At a financial institution, a fraud detection syztem identifies suspicious tranaactions and sends them to a specialist for review. The specialist reviews the transaction, the customer profile, and past history. If there is sufficient evidence of fraud, the tranaaction is blocked. Based on past history, the specialist blocks 40 percent of the suspicious tranactions. Assume a suspicious transaction is independent of other suspicious transactions. (a) Suppose the specialist will review 136 suspicious transactiona in one day. What is the expected number of blocked transactiona by the specialist? Show your work.
Note On your AP Exam, you will handwrite your responses to free-response questions in a test booklet
B I $\underline{U}$ $\square$ (b) Suppose the specialist wants to know the number of suspicious transactions that will need to be revieved until reaching the first transaction that will be blocked. (i) Define the random variable of interest and state how the variable is distributed. (ii) Determine the expected value of the random variable and interpret the expected value in context. $\square$ B I $\square$ (c) Consider a batch of 10 randomly selected suspicipus transactions. Suppose the specializt wants to know the probability that 2 of the ransactions will be blocked. (i) Define the random variable of interest and state how the variable is distributed. (ii) Find the probability that 2 transactions in the batch will be blocked. Show your work.

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Problem 1113

(a) The standard normal curve is graphed below. Shade the region under the standard norm $z=-0.50$ . (b) Use this table or the ALEKS calculator to find the area under the standard normal curve to $t$ Give your answer to four decimal places (for example, 0.1234).

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Problem 1114

Of the 44 plays attributed to a playwright, 14 are comedies, 13 are tragedies, and 17 are histories. If one play is selected at random, find the odds in favor of selecting a history.
The odds in favor of selecting a history are $\square$ $\square$ (Simplify your answer.)

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Problem 1115

A variable is normally distributed with mean 20 and standard deviation 3 . Use your graphing calculator to find each of the following areas. Write your answers in decimal form. Round to the nearest thousandth as needed. a) Find the area to the left of 20. $\square$ b) Find the area to the left of 16. $\square$ c) Find the area to the right of 17. $\square$ d) Find the area to the right of 26 . $\square$ e) Find the area between 16 and 29. $\square$

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Problem 1116

Of the last 60 people who went to the cash register at a department store, 13 had blond hair, 14 had black hair, 25 had brown hair, and 8 had red hair. Determine the experimental probability that the next person to come to the cash register has blond hair. $P($ blond $)=$ $\square$ (Simplify your answer.)

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Problem 1117

The spinner at the right is divided into eight equal parts. Find the theoretical probability of landing on the given section(s) of the spinner.
P(even) $P($ even $)=\square$ (Simplify your answer.)

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Problem 1118

[Questions 1-2] A study found that the duration of professional baseball games is uniformly distributed between 150 minutes and 250 minutes. Assume that Buffalo Bisons and Rochester Red Wings are playing tonight. A:'50 min B250 min
1. What is the probability that the duration of the tonight's game is exactly 150 minutes? A) $\frac{1}{250}$ B) $\frac{1}{150}$ C) $\frac{1}{100}$ D) 0.50 [Answer: $\qquad$ 1
2. What is the probability that the duration of the tonight's game is between 200 and 220 minutes? A) $\frac{1}{250}$ B) $\frac{1}{100}$ C) 0.20 D) $50 \%$ [Answer: $\qquad$ 1

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Problem 1119

13. The distribution of cholesterol levels in teenage boys is approximately normal with $\mu=170$ and $\sigma=$ 30. Levels above 200 warrant attention. Find the probability that a teenage boy has a cholesterol level greater than 200. A) 0.3419 B) 0.2138 C) 0.8413 D) 0.1587

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Problem 1120

OUESTION FIVE( 20 MARKS) (5 marks) a) Suppose you play a game that you can only either win or lose. The probability that you win game is $55 \%$ , and the probability that you lose is $45 \%$ , what is the probability that you win; i) 15 times if you play the game 20 times? (3 marks) ii) between 16 and 18 of all 20 games? (3 marks) b) Suppose a given website receives an average of 20 visitors per hour. What is the probability that number of visitors received by the website is; i) At least 4 in an hour? (2 marks) ii) Exactly 15 in three hours? (3 marks) c) The final exam scores in a statistics class were normally distributed with a mean of 63 an standard deviation of 5 . i) Find the probability that a randomly selected student scored more than 65 or * Google Chrome

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Problem 1121

Counting and Probability Outcomes and event probability
A coin is tossed three times. An outcome is represented by a string of the sort HTT (meaning a head on the first toss, followed by two tails). The 8 outcomes are listed in the table below. Note that each outcome has the same probability. For each of the three events in the table, check the outcome(s) that are contained in the event. Then, in the last column, enter the probability of the event.

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Problem 1122

8.2.3 Qulz: Using Probability to Make Decisions
Question 8 of 10 Two friends argue over who brushes their teeth more often. To settle the argument, they keep track of the number of mornings and nights they brush and calculate a probability. These are shown in the table. \begin{tabular}{|c|c|c|} \hline & Braxton & Arabella \\ \hline \begin{tabular}{c} Probability of brushing \\ in morning \end{tabular} & 0.79 & 0.85 \\ \hline \begin{tabular}{c} Probability of brushing \\ in evening \end{tabular} & 0.81 & A \\ \hline \end{tabular}
Who is more likely to brush both morning and evening? Assume all events are independent.

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Problem 1123

Part 6 of 6 Points: $0 \%$ , 9 of 10 points Save
Color blindness is an inherited characteristic that is more common in males than in females. If M represents male and C represents red-green color blindness, using the relative frequencies of the incidences of males and red-green color blindness as probabilities results in the values below. Complete parts (a) through ( $f$ ) below. $P(C)=0.035, P(M \cap C)=0.033, P(M \cup C)=0.487$ (a) Find $P\left(C^{\prime}\right)$ . $P\left(C^{\prime}\right)=0.965$ (Type an integer or a decimal.) (b) Find $P(M)$ . $P(M)=0.485$ (Type an integer or a decimal.) (c) Find $P\left(M^{\prime}\right)$ . $P\left(M^{\prime}\right)=0.515$ (Type an integer or a decimal.) (d) Find $P\left(M^{\prime} \cap C^{\prime}\right)$ . $P\left(M^{\prime} \cap C^{\prime}\right)=0.513$ (Type an integer or a decimal.) (e) Find $P\left(C \cap M^{\prime}\right)$ . $P\left(C \cap M^{\prime}\right)=0.002$ (Type an integer or a decimal.) (f) Find $P\left(C \cup M^{\prime}\right)$ . $P\left(C \cup M^{\prime}\right)=\square_{4}$ (Type an integer or a decimal.)

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Problem 1124

In the provided box, type in the two Capital letters and one word used by our textbook that fill in the blanks. Separate each with a space. Spelling of the word counts. For example: $X$ connects $Y$
The notation for conditional probability is $(P(B \mid A)$ which reads as the conditional probability of event $\qquad$ will occur $\qquad$ that the event $\qquad$ has already occurred.
Type your answer here $\square$

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Problem 1125

Determine whether the outcome is a Type I error, a Type II error, or a correct decision. A test is made of $H_{0}: \mu=15$ versus $H_{1}: \mu>15$ . The true value of $\mu$ is 17 , and $H_{0}$ is not rejected.
The outcome of the test is a (Choose one) Type I error correct decision Type II error

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Problem 1126

Use the information in the Table 3.19 to answer the next eight exercises. The table shows the political party affiliation of each of 67 members of the US Senate in June 2012, and when they are up for reelection. \begin{tabular}{|l|l|l|l|l|} \hline Up for reelection: & Democratic Party & Republican Party & Other & Total \\ \hline November 2014 & 20 & 13 & 0 & \\ \hline November 2016 & 10 & 24 & 0 & \\ \hline Total & & & & \\ \hline \end{tabular}
Table 3.19 101.
What is the probability that a randomly selected senator has an "Other" affiliation? 102.
What is the probability that a randomly selected senator is up for reelection in November 2016? Access for free at https://openstax.org 103.
What is the probability that a randomly selected senator is a Democrat and up for reelection in November 2016? 104.
What is the probability that a randomly selected senator is a Republican or is up for reelection in November 2014?

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Problem 1127

Exercice 2 PARTIE A Le système d'alarme d'une entreprise fonctionne de telle sorte que, si un danger se présente, l'alarme s'active avec une probabilité de 0,97 . La probabilité qu'un danger se présente est de 0,01 et la probabilité que l'alarme s'active est de 0,01465 . On note $A$ l'évènement «l'alarme s'active» et $D$ l'événement «un danger se présente ». On note $\bar{M}$ l'évènement contraire d'un évènement $M$ et $P(M)$ la probabilité de l'évènement $M$ .
1. Représenter la situation par un arbre pondéré qui sera complété au fur et à mesure de l'exercice.
2. a. Calculer la probabilité qu'un danger se présente et que l'alarme s'active. b. En déduire la probabilité qu'un danger se présente sachant que l'alarme s'active. Arrondir le résultat à $10^{-3}$ .
3. Montrer que la probabilité que l'alarme s'active sachant qu'aucun danger ne s'est présenté est 0,005 .
4. On considère qu'une alarme ne fonctionne pas normalement lorsqu'un danger se présente et qu'elle ne s'active pas ou bien lorsqu'aucun danger ne se présente et qu'elle s'active. Montrer que la probabilité que l'alarme ne fonctionne pas normalement est inférieure à 0,01 . PARTIE B Une usine fabrique en grande quantité des systèmes d'alarme. On prélève successivement et au hasard 5 systèmes d'alarme dans la production de l'usine. Ce prélèvement est assimilé à un tirage avec remise. On note $S$ l'évènement «l'alarme ne fonctionne pas normalement» et on admet que $P(S)=0,00525$ . On considère $X$ la variable aléatoire qui donne le nombre de systèmes d'alarme ne fonctionnant pas normalement parmi les 5 systèmes d'alarme prélevés. Les résultats seront arrondis à $10^{-4}$ .
1. Donner la loi de probabilité suivie par la variable aléatoire $X$ et préciser ses paramètres.
2. Calculer la probabilité que, dans le lot prélevé, un seul système d'alarme ne fonctionne pas normalement.
3. Calculer la probabilité que, dans le lot prélevé, au moins un système d'alarme ne fonctionne pas normalement.
PARTIE C Soit $n$ un entier naturel non nul. On prélève successivement et au hasard $n$ systèmes d'alarme. Ce prélèvement est assimilé à un tirage avec remise. Déterminer le plus petit entier $n$ tel que la probabilité d'avoir, dans le lot prélevé, au moins un système d'alarme qui ne fonctionne pas normalement soit supérieure à 0,07 .
Exercice 3 Partie A : études de deux fonctions On considère les deux fonctions $f$ et $g$ définies sur l'intervalle $[0 ;+\infty[$ par : $f(x)=0,06\left(-x^{2}+13,7 x\right) \quad \text { et } \quad g(x)=(-0,15 x+2,2) \mathrm{e}^{0,2 x}-2,2 \text {. }$
On admet que les fonctions $f$ et $g$ sont dérivables et on note $f^{\prime}$ et $g^{\prime}$ leurs fonctions dérivées respectives.
1. On donne le tableau de variations complet de la fonction $f$ sur l'intervalle $[0 ;+\infty[$ . \begin{tabular}{|c|ccc|} \hline $x$ & 0 & 6,85 & $+\infty$ \\ \hline $f(x)$ & & & $f(6,85)$ \\ & & & \\ \hline \end{tabular}

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Problem 1128

Let $S=\left\{E_{1}, E_{2}, E_{3}, E_{4}\right\}$ be the sample space of an experiment. Event $A=\left\{E_{1}, E_{2}\right\}$ . Event $B=\left\{E_{3}\right\}$ . Event $C=\left\{E_{2}, E_{3}\right\}$ . The probabilities of the sample points are assigned as follows: \begin{tabular}{cc} \hline Sample point & Probability \\ \hline $E_{1}$ & 0.1374 \\ $E_{2}$ & 0.1301 \\ $E_{3}$ & 0.1854 \\ $E_{4}$ & 0.5471 \\ \hline \end{tabular}
Then, the events $A$ and $B$ are independent.
Select one: a. False b. True

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Problem 1129

A variable $x$ is normally distributed with mean 24 and standard deviation 9. Round your answers to the nearest hundredth as needed. a) Determine the $z$ -score for $x=29$ . $z=0.56 \quad>0^{\infty}$ b) Determine the $z$ -score for $x=23$ . $z=$ c) What value of $x$ has a $z$ -score of 0.67 ? $x=\square$
Enter an integer or decimal number [more.. d) What value of $x$ has a $z$ -score of 0 ? $x=24 \quad$ e) What value of $x$ has a $z$ -score of 0 ? $x=24 \quad 0^{\circ}$

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Problem 1130

A spinner with 5 equally sized slices has 2 red slices, 2 yellow slices, and 1 blue slice. Kala spun the dial 1000 times and got the following results. \begin{tabular}{|c|c|c|c|} \hline Outcome & Red & Yellow & Blue \\ \hline Number of Spins & 391 & 410 & 199 \\ \hline \end{tabular}
Answer the following. Round your answers to the nearest thousandths. (a) From Kala's results, compute the experimental probability of landing on blue.
(b) Assuming that the spinner is fair, compute the theoretical probability of landing on blue. $\square$ (c) Assuming that the spinner is fair, choose the statement below that is true. will be close to the theoretical probability.

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Problem 1131

Determine the probability distribution's missing value. The probability that a tutbr will see $0,1,2,3$ , or 4 students \begin{tabular}{r|r|r|r|r|r} $x$ & 0 & 1 & 2 & 3 & 4 \\ \hline $P(x)$ & $\frac{1}{22}$ & $\frac{1}{11}$ & $\frac{1}{22}$ & $?$ & $\frac{1}{22}$ \end{tabular} A. $-\frac{5}{11}$ B. $\frac{17}{22}$ C. $\frac{1}{22}$ D. $\frac{9}{11}$

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Problem 1132

A bag has 20 papers numbered 1 to 20. Find the probability all three drawn numbers are even with (a) replacement and (b) no replacement.

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Problem 1133

Find the probability of picking a walnut first and an almond second from 13 almonds, 8 walnuts, and 19 peanuts.

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Problem 1134

Find the probability of picking a vowel first and a consonant second from cards with letters $M, A, R, B, L, E$ .

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Problem 1135

Find the probability of drawing 'p' first and 's' second from a sack of 26 letters. What is P(A and B)?

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Problem 1136

A bag has 20 papers numbered 1 to 20. Find the probability that 3 drawn numbers are even: (a) with replacement, (b) without replacement.

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Problem 1137

Find the missing probability $P(3)$ in the distribution where $P(0) = 0.2$ , $P(1) = 0.45$ , $P(2) = 0.3$ .

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Problem 1138

Find the missing probability for 29 students and calculate the mean and standard deviation for the Statistics classes.

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Problem 1139

A grocery store has 6 self-checkout stations. Given the probability distribution, find:
a. $P(3<X<5)=$ (Round to 2 decimals) b. $P(2 \leq X<4)=$ (Round to 2 decimals) c. $P(X \leq 5)=$ (Round to 2 decimals)

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Problem 1140

An accounting office has 6 phone lines. Use the probability table to find:
a. $P(X=4)=$ (2 decimals) b. $P(1<X \leq 3)=$ (2 decimals) c. $P(X \leq 5)=$ (2 decimals)

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Problem 1141

Survey data on college seniors' major changes is given. Find the probabilities for these scenarios:
a. At least 1 change: $P(x \geq 1)$ b. Fewer than 2 changes: $P(x < 2)$ c. More than 3 changes: $P(x > 3)$

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Problem 1142

Find the cumulative probability distribution (cdf) for the given values of $x$ and $P(x)$ :
$x$ : 0, 1, 2, 3, 4; $P(x)$ : 0.244, 0.238, 0.259, 0.229, 0.03.

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Problem 1143

A cookie brand has a probability distribution for daily sales. Answer these:
1. Find $P(15)$ .
2. Calculate expected sales.
3. Determine variance.

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Problem 1144

A jar has 53 marbles: 8 red, 21 blue, 24 green. Find the expected outcome and profitability of drawing a marble.

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Problem 1145

In a coin game, you start betting \$1, doubling after each loss. With a bankroll of \$127, what’s your expected profit?

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Problem 1146

What is the probability that Heads is winning after 10 flips if Tails is flipped first?

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Problem 1147

Korvis on 12 heledat ja 8 tumedat pardipoega. Ema võtab 4. Leia tõenäosus, et: a. kõik on heledad b. kõik on tumedad c. 2 on heledad ja 2 on tumedad.

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Problem 1148

In Mr. Martin's class of 8 students, find the probabilities for events A (Music Club) and B (Softball Club):
1. $P(A)$
2. $P(B)$
3. $P(A \text{ and } B)$
4. $P(A \text{ or } B)$
5. $P(A) + P(B) - P(A \text{ and } B)$

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Problem 1149

In Ms. Kim's class of 11 students, find probabilities for events $A$ (Chess Club) and $B$ (Math Club) using given data.
(a) Calculate: $P(A)=\square, \quad P(B)=\square, \quad P(A \text{ or } B)=\square, \quad P(A \text{ and } B)=\square, \quad P(A)+P(B)-P(A \text{ and } B)=\square$

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Problem 1150

Find the probability that the sample mean exceeds 80 for $\mu=75$ and $\sigma=12$ . Options: 2.5, 0.0062, 0.9938, 0.065.

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Problem 1151

Find the probability that the sample mean exceeds 80 given $m u=75$ and $\sigma=12$ .

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Problem 1152

What hidden variable explains why ice cream eaters drown more? Check all: A. Kids eat more ice cream. B. Age C. Warmer climates lead to more ice cream and swimming. D. Ice cream amount.

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Problem 1153

Identify possible hidden variables for the statement: "People who drink coffee are more likely to develop cancer." Options: A. Cars, B. Coffee amount, C. Sample selection, D. Age.

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Problem 1154

What is the probability of getting 0 heads and 3 tails when flipping 3 fair coins? Round to the thousandths or give as a fraction.

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Problem 1155

Find the probability of rolling a sum of 6 with two dice. Enter as a fraction or decimal rounded to 3 decimal places. $P(\text{sum of } 6) =$

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Problem 1156

Find the probability of rolling two dice and getting a sum of 6 or 5/12. Round to 3 decimal places.

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Problem 1157

In the probability distribution to the right, the random variable X represents the number of hits a baseball player obtained in a game over the course of a season. Complete parts (a) through (f) below. \begin{tabular}{cc} $\mathbf{x}$ & $\mathbf{P ( x )}$ \\ \hline 0 & 0.1662 \\ 1 & 0.3355 \\ 2 & 0.2851 \\ 3 & 0.1494 \\ 4 & 0.0389 \\ 5 & 0.0249 \\ \hline \end{tabular} (a) Verify that this is a discrete probability distribution.
This is a discrete probability distribution because $\square$ between 0 and $\square$ inclusive, and the $\square$ sum of the probabilities is 1. (Type whole numbers. Use ascending order.)

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Problem 1158

g. $P(z \leq-0.83$ given $z \leq 0)=$ h. $P(z<-1.79$ or $z \geq 2.21)=$ $\square$ i. $P(z<0.6$ or $z \geq 0.3)=$ $\square$ j. $P(z=-1.79)=$ $\square$

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Problem 1159

The given jar contains yellow ( $Y$ ), blue (B), and red (R) balls. Anne randomly chooses a single ball from the can shown here. Find the odds against the event. red or yellow ( R or Y )
State the odds against red or yellow in lowest terms. The odds against red or yellow are $\square$ to $\square$ (Type whole numbers.)

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Problem 1160

Inis question: 3 point(s) possible Submit quiz
For the experiment of drawing a single card from a standard 52-card deck, find (a) the probability of the given event, and (b) the oc in favor of the given event. not a four (a) The probability is $\square$ (Type an integer or a simplified fraction.) (b) The odds, in simplified form, in favor of the event of the card not being a four, are $\square$ to $\square$ .

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Problem 1161

AA www-awy.aleks.com Data Analysis and Probability Identifying outcomes in a random number table used to simulate a simpl... Sophia Español
The winners of a carnival game draw a ticket from a box to determine their prize. Each winner draws a ticket and places it back into the box before the next draw. Every winner has a $17 \%$ chance of getting a pencil pouch, a $34 \%$ chance of getting a backpack, and a $49 \%$ chance of getting a gumball.
The game operator wants to simulate what could happen for the next ten winners. So for each winner, she generates a random whole number from 1 to 100 . She lets 1 to 17 represent a winner getting a pencil pouch, 18 to 51 a backpack, and 52 to 100 a gumball. Here is the game operator's simulation. \begin{tabular}{|c|c|c|c|c|c|c|c|c|c|c|} \hline Winner & 1 & 2 & 3 & 4 & 5 & 6 & 7 & 8 & 9 & 10 \\ \hline Random number & 30 & 37 & 69 & 17 & 36 & 74 & 26 & 52 & 27 & 58 \\ \hline \end{tabular}
In the simulation, which prize did each winner get? (a) Winner 4: (Choose one) (b) Winner 6: (Choose one) (c) Winner 9: (Choose one) Explanation Check

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Problem 1162

The distribution of blood types for 100 Americans is listed in the table. If one donor is selected at random, find the probability of selecting a person with blood type $A+$ or $A$ - \begin{tabular}{r|rrrrrrrr} Blood Type & $\mathrm{O}+$ & $\mathrm{O}-$ & $\mathrm{A}+$ & $\mathrm{A}-$ & $\mathrm{B}+$ & $\mathrm{B}-$ & $\mathrm{AB}+$ & $\mathrm{AB}-$ \\ \hline Number & 37 & 6 & 34 & 6 & 10 & 2 & 4 & 1 \end{tabular} A. 0.4 B. 0.34 C. 0.02 D. 0.06

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Problem 1163

Researchers thinks that two plant species depend on each other. Wherever one grows, many times they observe that the other plant grows there as well.
What's the null hypothesis? The two plants are independent. The two plants are not independent.

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Problem 1164

Suppose that the genders of the three children of a family are soon to be revealed. An outcome is represented by a string of the sort GBB (meaning the oldest child is a girl, the second oldest is a boy, and the youngest is a boy).
The 8 outcomes are listed below. Assume that each outcome has the same probability. Complete the following. Write your answers as fractions, (a) Check the outcomes for each of the three events below. Then, enter the probability of each event. \begin{tabular}{|c|c|c|c|c|c|c|c|c|c|} \hline & \multicolumn{8}{|c|}{Outcomes} & \multirow[b]{2}{}{Probability} \\ \hline & BBB & BBG & BGB & B GG & GBB & GBG & GGB & G G G & \\ \hline Event X: The last child is a boy & ■ & — & ■ & ㅁ & ■ & ■ & — & 0 & — \\ \hline Event Y: Exactly one child is a girl & ■ & — & ■ & $\square$ & 0 & — & ■ & ■ & — \\ \hline Event $X$ and $Y$ : The last child is a boy and exactly one child is a girl & ■ & ■ & 口 & ■ & ■ & ■ & ■ & — & — \\ \hline \end{tabular} (b) Suppose exactly one child is a girl. (That is, Event $Y$ occurs.) This will limit the possible outcomes. From the remaining outcomes, check the outcomes for Event $X$ . Then, enter the probability that Event $X$ occurs given that Event $Y$ occurs. \begin{tabular}{|l|c|c|c|c|c|c|c|c|c|} \cline { 2 - 8 } \multicolumn{1}{c|}{} & \multicolumn{6}{c|}{ Outcomes given exactly one child is a girl } & \multirow{2}{}{ Probability } \\ \cline { 2 - 8 } \multicolumn{1}{c|}{} & $B B G$ & $B G B$ & & $G B B$ & & & \\ \hline Event $X$ : The last child is a boy & & $\square$ & $\square$ & & $\square$ & & & & $\square$ \\ \hline \end{tabular} (c) Give the following probabilities and select the correct option below. $\begin{array}{c} \frac{P(X \text { and } Y)}{P(Y)}=\square \\ P(X \mid Y)=\square \\ \frac{P(X \text { and } Y)}{P(Y)} ? P(X \mid Y) \end{array}$

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Problem 1165

A fair coin is tossed three times in succession. The set of equally likely outcomes is $\{\mathrm{HHH}, \mathrm{HHT}, \mathrm{HTH}, \mathrm{THH}, \mathrm{HIT}$ , THT, THH, TIT\}. Find the probability of getting exactly zero heads.
The probability of getting zero heads is $\square$ (Type an integer or a simplified fraction.)

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Problem 1166

A consumer group is investigating the number of flights at a certain airline that are overbooked. They conducted a simulation to estimate the probability of overbooked flights in the next 5 flights. The results of 1,000 trials are shown in the following histogram.
Based on the histogram, what is the probability that at least 4 of the next 5 flights at the airline will be overbooked?

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Problem 1167

According to a study published in a reputable science magazine, about 6 women in 100,000 have cervical cancer (C), so $\mathrm{P}(\mathrm{C})=0.00006$ . Suppose the chance that a Pap smear will detect cervical cancer when it is present is 0.89 . Therefore, $\mathrm{P}($ test pos $\mid \mathrm{C})=0.89$ . What is the probability that a randomly chosen woman who has this test will both have cervical cancer AND test positive for it? $\mathrm{P}($ have C AND test positive $)=$ $\square$ (Round to six decimal places as needed.)

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Problem 1168

which had more stable prices. \begin{tabular}{|c|c|c|c|c|c|} \hline Prices in. city A & 20 & 22 & 19 & 23 & 18 \\ \hline Prices in city B & 13 & 14 & 16 & 12 & 15 \\ \hline \end{tabular}
Wildlife biologists have determined that the tail of dwarf pygmy wombats on the game reser normally distributed with mean of 42 cm and standard deviation of 5 cm . i. What percentage of dwarf pygmy wombat has tails that are 45 cm long or shorter (4 Marks) ii. What percentage of dwarf pygmy wombat has tails that are 54 cm long or longer? (4 Marks) iii. What tail length would put a wombat in the top $13 \%$ of the distribution?

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Problem 1169

UESTION FOUR ( 20 MARKS ) The length of life of an instrument produced by a machine has a normal distribution with a mean of 12 months and standard deviation of 2 months. Find the probability that in a random sample of 4 instrument produced by this machine, the average length of life i) less than 10.5 months. (3 Marks) ii) between 11 and 13 months (4 Marks) iii) greater than 15 months (3 Marks)

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Problem 1170

Let $S=\left\{E_{1}, E_{2}, E_{3}, E_{4}\right\}$ be the sample space of an experiment. Event $A=\left\{E_{1}, E_{2}\right\}$ . Event $\underline{B}=\left\{E_{3}\right\}$ . Event $C=\left\{E_{2}, E_{3}\right\}$ . The probabilities of the sample points are assigned as follows: \begin{tabular}{cc} \hline Sample point & Probability \\ \hline $E_{1}$ & 0.1979 \\ $E_{2}$ & 0.1273 \\ $E_{3}$ & 0.2114 \\ $E_{4}$ & 0.4634 \\ \hline \end{tabular}
Then, $P\left(B^{c}\right)$ is equal to Select one: a. 0.8727 b. 0.6613 C. 0.7886 d. 0.6748 e. 0.5907 f. 0.4634 g. 1.0000

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Problem 1171

The data given below were taken from a study about the preferred payment method (Cash or Credit card). The table below indicates the numbers of people in the study according to their gender and preferred payment method. \begin{tabular}{ccc} & Cash & Credit Card \\ Men & 141 & 260 \\ Women & 206 & 393 \end{tabular}
If a person is selected at random, what is the probability that the person is a man or prefers the cash payment method?

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Problem 1172

Angemessene Anzahl von Bankautomaten ermitteln Im Rahmen einer Umbaumaßnahme einer Bank sollen im Vorraum Automaten zum Ausdrucken von Kontoauszügen aufgestellt werden. Das Drucken dauert im Mittel eine Minute. Während der Hauptgeschäftszeit benutzen in einer Stunde 120 Kunden einen solchen Automaten. a) Erläutern Sie, welche vereinfachenden Annahmen notwendig sind, damit der Vorgang als 120-stufiges BERNOULLI-Experiment mit der Erfolgswahrscheinlichkeit $p=\frac{1}{60}$ modelliert werden kann. b) Bestimmen Sie mit dem Ansatz aus Teilaufgabe a) die Wahrscheinlichkeiten dafür, dass zu einem beliebigen Zeitpunkt kein Automat, genau ein Automat, genau zwei, drei, vier, ... Automaten benötigt werden. Berechnen Sie hieraus die Wahrscheinlichkeit, dass die Ausstattung mit zwei, drei, vier, fünf Automaten ausreicht. c) Überlegen Sie, welche Gesichtspunkte bei einer solchen Modellierung nicht berücksichtigt bzw. vernachlässigt werden (Modellkritik).

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Problem 1173

$\text{The random variable } X \text{ represents the number of children per family in a rural area in Ohio, with the probability distribution: } p(x)=0.05 x, \quad x=2,3,4,5, \text{ or } 6.$
1. Express the probability distribution in a tabular form. \begin{tabular}{|c|c|c|c|c|c|} \hline X & 2 & 3 & 4 & 5 & 6 \\ \hline P(X) & & & & & \\ \hline \end{tabular}
4. Find the following probabilities: \begin{itemize} \item[a.] $P(X \geq 4)$ \item[b.] $P(X>4)$ \item[c.] $P(3 \leq X \leq 5)$ \end{itemize}

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Problem 1174

2. For a normal distribution with a mean of $\mu=40$ and $\sigma=4$ , what is the probability of selecting an individual with a score greater than 46 ? (a.) 0.0668

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Problem 1175

Random Variables and Distributions Normal distribution: Finding a probalility, baste
A certain test is designed to measure the satisfaction of an individual with his/her relationship. Suppose that the scores on this test are approxima distributed with a mean of 50 and a standard deviation of 8 . An individual with a score of 35 or less is considered dissatisfied with his/her relation to this criterion, what proportion of people in relationships are dissatisfied? Round your answer to at least four decimal places. $\square$

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Problem 1176

Consider the probability that no more than $98$ out of $125$ DVDs will malfunction. Assume the probability that a given DVD will malfunction is $2\%$ . Specify whether the normal curve can be used as an approximation to the binomial probability by verifying the necessary conditions. Answer 2 Points Yes No Keypad Keyboard Shortcut

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Problem 1177

1 2 3 4 5 6 7 8 9 10
Marcia has two credit cards and would like to consolidate the two balances into one balance on the card with the lower interest rate. The table below shows the information about the two credit cards Marcia currently uses. \begin{tabular}{|l|c|c|} \hline & Card A & Card B \\ \hline Amount & $\$ 1,389.47$ & $\$ 1,065.32$ \\ \hline APR & $16 \%$ & $12 \%$ \\ \hline Monthly Payment & $\$ 39.38$ & $\$ 28.05$ \\ \hline \hline \end{tabular}
After 4 years, approximately how much will Marcia have saved in interest by consolidating the two balances? a. $\$ 1,890.24$ b. $\$ 133.92$ c. $\$ 543.84$ d. $\$ 1,346.40$
Please select the best answer from the choices provided.

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Problem 1178

The table shows the outcomes of rolling two number cube finding the product of the two numbers. Use the table for
6. What is the theoretical probability of rolling a product greater than 12? 15
7. If Alan rolls two number cubes three hundred times, about how many times would he expect a product greater than 12? Round to the nearest whole number. 142

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Problem 1179

The following table gives a two-way classification of the responses.
| | Should be paid, PAID | Should not be paid, $\overline{PAID}$ | Total | |---------------------|----------------------|-----------------------------------|-------| | Student athlete, SA | 90 | 10 | 100 | | Student non-athlete, SNA | 210 | 90 | 300 | | Total | 300 | 100 | 400 |
a) If one student is randomly selected from these 400 students, find the probability that this student
i. Is in favour of paying college athletes $P(PAID) =$
ii. Favours paying college athletes given that the student selected is a non-athlete $P(PAID | SNA) =$
iii. Is an athlete and favours paying student athletes $P(SA \cap PAID) =$
iv. Is a non-athlete or is against paying student athletes $P(SNA \cup \overline{PAID}) =$

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Problem 1180

Find the probability that a randomly chosen American has type B blood, given that $15\%$ of Americans have type B.

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Problem 1181

Find the probability that a random American has type B blood ( $15\%$ ) and the probability of having type A or B.

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Problem 1182

A teacher gives three test versions. Find these probabilities: a. $P($ pass $\mid$ Test A) $and b.$ P( $Test C$ \mid $fail)$ .

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Problem 1183

What is the probability that a randomly selected revenue source comes from excise or other taxes, given the percentages? $P($ excise or other taxes $)=$

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Problem 1184

Find the probability of randomly selecting a school with 100 or fewer computers. Round to 3 decimal places.

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Problem 1185

Find the probability of drawing a purple marble from a bag with 4 red, 6 purple, 9 blue, 3 green, and 2 yellow marbles.

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Problem 1186

Find the probability of drawing a red marble from a bag with 4 red, 6 purple, 9 blue, 3 green, and 2 yellow marbles.

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Problem 1187

What is the probability that Ava is assigned the numbers 1, 5, or 10 out of 16 possible tryout numbers?

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Problem 1188

Find the probability of randomly selecting an apple, orange, banana, plum, or nectarine from a basket with 8 apples, 4 oranges, 3 bananas, 6 plums, and 11 nectarines.

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Problem 1189

Find the probability of randomly choosing an apple or plum from a basket with 8 apples, 6 plums, and more fruit. $P($ apple or plum $)$

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Problem 1190

Find the probability that a randomly opened page in a 50-page book is greater than 30 ( $P(>30)$ ) and is a prime number ( $P(prime)$ ).

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Problem 1191

Find the probability that a spinner lands on a number less than 10 when spun, given 9 out of 12 sections meet this condition.

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Problem 1192

Find the percentage of scores between 158 and $872$ in a normal distribution with mean 515 and std dev 119.

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Problem 1193

A standardized test's math scores have a mean of 515 and a standard deviation of 119. Find the percentages for the given ranges.

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Problem 1194

A standardized test has scores with a mean of 515 and a standard deviation of 119. Find the percentages for parts (a), (b), and (c).

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Problem 1195

Max threw darts 20 times: 12 hits at 10 points, 6 at 25 points, and 2 at 50 points. Find the probability of his next throw.

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Problem 1196

Find the probability of choosing a date in June that is odd and a multiple of 3, and after the 16th of June.

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Problem 1197

Find the probability of Michael Phelps choosing each type of medal: gold, silver, and bronze, given he has 23 gold, 3 silver, and 2 bronze.

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Problem 1198

Find the probability of selecting an apple or a plum from a basket containing 8 apples, 4 oranges, 3 bananas, 6 plums, and 11 nectarines. Calculate $P$ (apple or plum).

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Problem 1199

Find the probabilities of selecting a 1 cent stamp, $P(1 \text{ cent})$ , and at least a 21 cent stamp, $P(\text{at least 21 cent})$ .

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Problem 1200

In the 2023 US Open, 128 players compete in Women's Singles, with 24 being American. What is the probability an American wins? Answer as a fraction or $\%$ (rounded to the nearest tenth, e.g., $10.6\%$ ).

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1 ...9 10 11 12 13 14 15 16

Probability

Problem 1101

Problem 1102

What is the term for patients feeling better after a sugar pill for headaches? A. randomization B. control C. experimental D. placebo.

Problem 1103

∨1\vee 1∨1 12 3 4 5 6 ✓7\checkmark 7✓7 78If P(A)=0.51,P(B)=0.6P(A)=0.51, P(B)=0.6P(A)=0.51,P(B)=0.6, and P(AP(AP(A and B)=0.41B)=0.41B)=0.41, find P(AP(AP(A or B)B)B). P(A or B)=P(A \text { or } B)=P(A or B)= □\square□ □\square□

Problem 1104

Problem 1105

Problem 1106

Problem 1107

Problem 1108

Problem 1109

Out of 160 workers surveyed at a company, 37 walk to work. a. What is the experimental probability that a randomly selected worker at that company walks to work? b. Predict about how many of the 4000 workers at the company walk to work. a. The experimental probability is □\square□

Problem 1110

Problem 1111

Problem 1112

Problem 1113

(a) The standard normal curve is graphed below. Shade the region under the standard norm z=−0.50z=-0.50z=−0.50. (b) Use this table or the ALEKS calculator to find the area under the standard normal curve to ttt Give your answer to four decimal places (for example, 0.1234).

Problem 1114

Of the 44 plays attributed to a playwright, 14 are comedies, 13 are tragedies, and 17 are histories. If one play is selected at random, find the odds in favor of selecting a history.The odds in favor of selecting a history are □\square□ □\square□ (Simplify your answer.)

Problem 1115

Problem 1116

Problem 1117

The spinner at the right is divided into eight equal parts. Find the theoretical probability of landing on the given section(s) of the spinner.P(even) P(P(P( even )=□)=\square)=□ (Simplify your answer.)

Problem 1118

Problem 1119

13. The distribution of cholesterol levels in teenage boys is approximately normal with μ=170\mu=170μ=170 and σ=\sigma=σ= 30. Levels above 200 warrant attention. Find the probability that a teenage boy has a cholesterol level greater than 200. A) 0.3419 B) 0.2138 C) 0.8413 D) 0.1587

Problem 1120

Problem 1121

Problem 1122

Problem 1123

Problem 1124

Problem 1125

Problem 1126

Problem 1127

Problem 1128

Problem 1129

Problem 1130

Problem 1131

Problem 1132

A bag has 20 papers numbered 1 to 20. Find the probability all three drawn numbers are even with (a) replacement and (b) no replacement.

Problem 1133

Find the probability of picking a walnut first and an almond second from 13 almonds, 8 walnuts, and 19 peanuts.

Problem 1134

Find the probability of picking a vowel first and a consonant second from cards with letters M,A,R,B,L,EM, A, R, B, L, EM,A,R,B,L,E.

Problem 1135

Find the probability of drawing 'p' first and 's' second from a sack of 26 letters. What is P(A and B)?

Problem 1136

A bag has 20 papers numbered 1 to 20. Find the probability that 3 drawn numbers are even: (a) with replacement, (b) without replacement.

Problem 1137

Find the missing probability P(3)P(3)P(3) in the distribution where P(0)=0.2P(0) = 0.2P(0)=0.2, P(1)=0.45P(1) = 0.45P(1)=0.45, P(2)=0.3P(2) = 0.3P(2)=0.3.

Problem 1138

Find the missing probability for 29 students and calculate the mean and standard deviation for the Statistics classes.

Problem 1139

A grocery store has 6 self-checkout stations. Given the probability distribution, find:a. P(3<X<5)=P(3<X<5)=P(3<X<5)= (Round to 2 decimals) b. P(2≤X<4)=P(2 \leq X<4)=P(2≤X<4)= (Round to 2 decimals) c. P(X≤5)=P(X \leq 5)=P(X≤5)= (Round to 2 decimals)

Problem 1140

An accounting office has 6 phone lines. Use the probability table to find:a. P(X=4)=P(X=4)=P(X=4)= (2 decimals) b. P(1<X≤3)=P(1<X \leq 3)=P(1<X≤3)= (2 decimals) c. P(X≤5)=P(X \leq 5)=P(X≤5)= (2 decimals)

Problem 1141

Survey data on college seniors' major changes is given. Find the probabilities for these scenarios: a. At least 1 change: P(x≥1)P(x \geq 1)P(x≥1) b. Fewer than 2 changes: P(x<2)P(x < 2)P(x<2) c. More than 3 changes: P(x>3)P(x > 3)P(x>3)

Problem 1142

Find the cumulative probability distribution (cdf) for the given values of xxx and P(x)P(x)P(x): xxx: 0, 1, 2, 3, 4; P(x)P(x)P(x): 0.244, 0.238, 0.259, 0.229, 0.03.

Problem 1143

A cookie brand has a probability distribution for daily sales. Answer these: 1. Find P(15)P(15)P(15).2. Calculate expected sales.3. Determine variance.

Problem 1144

A jar has 53 marbles: 8 red, 21 blue, 24 green. Find the expected outcome and profitability of drawing a marble.

Problem 1145

In a coin game, you start betting \$1, doubling after each loss. With a bankroll of \$127, what’s your expected profit?

Problem 1146

What is the probability that Heads is winning after 10 flips if Tails is flipped first?

Problem 1147

Korvis on 12 heledat ja 8 tumedat pardipoega. Ema võtab 4. Leia tõenäosus, et: a. kõik on heledad b. kõik on tumedad c. 2 on heledad ja 2 on tumedad.

Problem 1148

In Mr. Martin's class of 8 students, find the probabilities for events A (Music Club) and B (Softball Club):1. P(A)P(A)P(A)2. P(B)P(B)P(B)3. P(A and B)P(A \text{ and } B)P(A and B)4. P(A or B)P(A \text{ or } B)P(A or B)5. P(A)+P(B)−P(A and B)P(A) + P(B) - P(A \text{ and } B)P(A)+P(B)−P(A and B)

Problem 1149

Problem 1150

Find the probability that the sample mean exceeds 80 for μ=75\mu=75μ=75 and σ=12\sigma=12σ=12. Options: 2.5, 0.0062, 0.9938, 0.065.

Problem 1151

Find the probability that the sample mean exceeds 80 given mu=75m u=75mu=75 and σ=12\sigma=12σ=12.

Problem 1152

What hidden variable explains why ice cream eaters drown more? Check all: A. Kids eat more ice cream. B. Age C. Warmer climates lead to more ice cream and swimming. D. Ice cream amount.

$\vee 1$ 12 3 4 5 6 $\checkmark 7$ 78
If $P(A)=0.51, P(B)=0.6$ , and $P(A$ and $B)=0.41$ , find $P(A$ or $B)$ . $P(A \text { or } B)=$ $\square$ $\square$

Out of 160 workers surveyed at a company, 37 walk to work. a. What is the experimental probability that a randomly selected worker at that company walks to work? b. Predict about how many of the 4000 workers at the company walk to work. a. The experimental probability is $\square$

(a) The standard normal curve is graphed below. Shade the region under the standard norm $z=-0.50$ . (b) Use this table or the ALEKS calculator to find the area under the standard normal curve to $t$ Give your answer to four decimal places (for example, 0.1234).

Of the 44 plays attributed to a playwright, 14 are comedies, 13 are tragedies, and 17 are histories. If one play is selected at random, find the odds in favor of selecting a history.
The odds in favor of selecting a history are $\square$ $\square$ (Simplify your answer.)

The spinner at the right is divided into eight equal parts. Find the theoretical probability of landing on the given section(s) of the spinner.
P(even) $P($ even $)=\square$ (Simplify your answer.)

13. The distribution of cholesterol levels in teenage boys is approximately normal with $\mu=170$ and $\sigma=$ 30. Levels above 200 warrant attention. Find the probability that a teenage boy has a cholesterol level greater than 200. A) 0.3419 B) 0.2138 C) 0.8413 D) 0.1587

Find the probability of picking a vowel first and a consonant second from cards with letters $M, A, R, B, L, E$ .

Find the missing probability $P(3)$ in the distribution where $P(0) = 0.2$ , $P(1) = 0.45$ , $P(2) = 0.3$ .

A grocery store has 6 self-checkout stations. Given the probability distribution, find:
a. $P(3<X<5)=$ (Round to 2 decimals) b. $P(2 \leq X<4)=$ (Round to 2 decimals) c. $P(X \leq 5)=$ (Round to 2 decimals)

An accounting office has 6 phone lines. Use the probability table to find:
a. $P(X=4)=$ (2 decimals) b. $P(1<X \leq 3)=$ (2 decimals) c. $P(X \leq 5)=$ (2 decimals)

Survey data on college seniors' major changes is given. Find the probabilities for these scenarios:
a. At least 1 change: $P(x \geq 1)$ b. Fewer than 2 changes: $P(x < 2)$ c. More than 3 changes: $P(x > 3)$

Find the cumulative probability distribution (cdf) for the given values of $x$ and $P(x)$ :
$x$ : 0, 1, 2, 3, 4; $P(x)$ : 0.244, 0.238, 0.259, 0.229, 0.03.

A cookie brand has a probability distribution for daily sales. Answer these:
1. Find $P(15)$ .
2. Calculate expected sales.
3. Determine variance.

In Mr. Martin's class of 8 students, find the probabilities for events A (Music Club) and B (Softball Club):
1. $P(A)$
2. $P(B)$
3. $P(A \text{ and } B)$
4. $P(A \text{ or } B)$
5. $P(A) + P(B) - P(A \text{ and } B)$

Find the probability that the sample mean exceeds 80 for $\mu=75$ and $\sigma=12$ . Options: 2.5, 0.0062, 0.9938, 0.065.

Find the probability that the sample mean exceeds 80 given $m u=75$ and $\sigma=12$ .

Find the probability of rolling a sum of 6 with two dice. Enter as a fraction or decimal rounded to 3 decimal places. $P(\text{sum of } 6) =$

g. $P(z \leq-0.83$ given $z \leq 0)=$ h. $P(z<-1.79$ or $z \geq 2.21)=$ $\square$ i. $P(z<0.6$ or $z \geq 0.3)=$ $\square$ j. $P(z=-1.79)=$ $\square$

Researchers thinks that two plant species depend on each other. Wherever one grows, many times they observe that the other plant grows there as well.
What's the null hypothesis? The two plants are independent. The two plants are not independent.

2. For a normal distribution with a mean of $\mu=40$ and $\sigma=4$ , what is the probability of selecting an individual with a score greater than 46 ? (a.) 0.0668