Math  /  Data & Statistics

Questionww-awu-aleks.com Sports Boting and Onlin... Sports Boting Secret -.. 11/22/24 ATL @ CHI /1/St/ 1 / \mathrm{St}. Home - Northern Essex Content ALEKs - Jonathan Vega. ChatGPT (5) KaiCenat - 1 Homework 4:7(1,2,3,4)8(2,3,4)4: 7(1,2,3,4) 8(2,3,4) Question 16 of 40 (1 point) I Question Attempt 1 of 3 Jonathan
The probability that the sample mean score is less than 509 is 0.1841 0 Españ
Correct Answer:
The probability that the sample mean score is less than 509 is 0.1813 .
Part 2 of 5 (b) What is the probability that the sample mean score is between 486 and 525? Round the answer to at least four decimal places.
The probability that the sample mean score is between 486 and 525 is 0.5773
Part 3 of 5 (c) Find the 90th 90^{\text {th }} percentile of the sample mean. Round the answer to at least two decimal places.
The 90th 90^{\text {th }} percentile of the sample mean is 540.25 .
Part: 3/53 / 5
Part 4 of 5 (d) Using a cutoff of 0.05 , would it be unusual if the sample mean were greater than 525 ? Round the answer to at least four decimal places.
It \square (Choose one) be unusual if the sample mean were greater than 525 , since the probability is \square . Skip Part Check Save For Later Submit Assignment (a) 2024 McGraw Hill LLC. All Rights Reserved. Terms of Use I Privagy Center I Accessilbility

Studdy Solution

STEP 1

What is this asking? Given a bunch of info about sample means, we need to figure out if a sample mean greater than 525 is unusual, using a cutoff of 0.05. Watch out! Don't mix up "greater than" and "less than" when calculating probabilities!
Also, remember that "unusual" means the probability is *below* the cutoff.

STEP 2

1. Calculate the probability
2. Determine if it's unusual

STEP 3

From Part 2 of the problem, we know the probability that the sample mean score is between 486 and 525 is **0.5773**.

STEP 4

The total probability under a normal distribution curve is always **1**.

STEP 5

Since we're dealing with a continuous distribution, the probability of the sample mean being *exactly* 525 is essentially zero.
So, the probability of the sample mean being *less than* 525 is practically the same as the probability of it being *less than or equal to* 525.
We know the probability of the sample mean being between 486 and 525 is 0.5773.
While we don't have the probability of the sample mean being less than 486, we *do* know that the total probability of the sample mean being less than 525 must be greater than **0.5773**.

STEP 6

To find the probability of the sample mean being *greater* than 525, we subtract the probability of it being *less than* 525 from the total probability of **1**.
Since the probability of the sample mean being less than 525 is greater than 0.5773, the probability of the sample mean being *greater* than 525 must be *less than* 10.5773=0.42271 - 0.5773 = \textbf{0.4227}.

STEP 7

We're given a cutoff of **0.05**.
We just found that the probability of the sample mean being greater than 525 is less than **0.4227**.

STEP 8

Since 0.4227 is greater than 0.05, it would *not* be unusual if the sample mean were greater than 525.

STEP 9

It would *not* be unusual if the sample mean were greater than 525, since the probability is less than 0.4227, which is greater than the cutoff of 0.05.

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