Question7.- A pro shop has a probability distribution for golf ball orders. a) Find the probability of ordering at most 2 golf balls. b) Find the probability of ordering at least one golf ball. c) Find the mean.
8.- A teacher claims the mean height of 5-year-olds is more than 95 cm. a) State the null and alternative hypothesis. b) Find the test statistic. c) Find the P-value or critical points. d) Make a decision using P-value or critical values. e) State your conclusion.

Studdy Solution

STEP 1

Assumptions1. The number of golf balls ordered by customers has the given probability distribution. . The probability distribution is discrete.
3. The mean height and standard deviation of twenty5-year-old children are given.
4. The significance level for the hypothesis test is0.01.

STEP 2

To find the probability of ordering at most2 golf balls, we need to sum the probabilities of ordering1 or2 golf balls.
$(x \leq2) =(x=1) +(x=2)$

STEP 3

Plug in the given probabilities for ordering1 and2 golf balls to calculate the probability.
$(x \leq2) =0.14 +0.02$

STEP 4

Calculate the probability of ordering at most2 golf balls.
$(x \leq2) =0.14 +0.02 =0.16$

STEP 5

To find the probability of ordering at least one golf ball, we need to sum the probabilities of ordering1,2,3,4, or5 golf balls.
$(x \geq1) =(x=1) +(x=2) +(x=3) +(x=4) +(x=5)$

STEP 6

Plug in the given probabilities for ordering1,2,3,4, and5 golf balls to calculate the probability.
$(x \geq1) =0.14 +0.02 +0.36 +0.38 +0.10$

STEP 7

Calculate the probability of ordering at least one golf ball.
$(x \geq1) =0.14 +0.02 +0.36 +0.38 +0.10 =1$

STEP 8

To find the mean, we need to multiply each value of x by its corresponding probability and sum these products.
$\mu = \sum x \cdot(x)$

STEP 9

Plug in the given values for x and their corresponding probabilities to calculate the mean.
$\mu =\cdot.14 +2\cdot.02 +3\cdot.36 +4\cdot.38 +5\cdot.$

STEP 10

Calculate the mean.
$\mu =\cdot0.14 +2\cdot0.02 +3\cdot0.36 +4\cdot0.38 +5\cdot0.10 =3.56$ The probability of ordering at most2 golf balls is0.16, the probability of ordering at least one golf ball is, and the mean is3.56.

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Studdy Solution

STEP 1

Assumptions1. The number of golf balls ordered by customers has the given probability distribution. . The probability distribution is discrete.
3. The mean height and standard deviation of twenty5-year-old children are given.
4. The significance level for the hypothesis test is0.01.

STEP 2

To find the probability of ordering at most2 golf balls, we need to sum the probabilities of ordering1 or2 golf balls.
$(x \leq2) =(x=1) +(x=2)$

STEP 3

Plug in the given probabilities for ordering1 and2 golf balls to calculate the probability.
$(x \leq2) =0.14 +0.02$

STEP 4

Calculate the probability of ordering at most2 golf balls.
$(x \leq2) =0.14 +0.02 =0.16$

STEP 5

To find the probability of ordering at least one golf ball, we need to sum the probabilities of ordering1,2,3,4, or5 golf balls.
$(x \geq1) =(x=1) +(x=2) +(x=3) +(x=4) +(x=5)$

STEP 6

Plug in the given probabilities for ordering1,2,3,4, and5 golf balls to calculate the probability.
$(x \geq1) =0.14 +0.02 +0.36 +0.38 +0.10$

STEP 7

Calculate the probability of ordering at least one golf ball.
$(x \geq1) =0.14 +0.02 +0.36 +0.38 +0.10 =1$

STEP 8

To find the mean, we need to multiply each value of x by its corresponding probability and sum these products.
$\mu = \sum x \cdot(x)$

STEP 9

Plug in the given values for x and their corresponding probabilities to calculate the mean.
$\mu =\cdot.14 +2\cdot.02 +3\cdot.36 +4\cdot.38 +5\cdot.$

STEP 10

Calculate the mean.
$\mu =\cdot0.14 +2\cdot0.02 +3\cdot0.36 +4\cdot0.38 +5\cdot0.10 =3.56$ The probability of ordering at most2 golf balls is0.16, the probability of ordering at least one golf ball is, and the mean is3.56.

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Studdy Solution

STEP 1

Assumptions1. The number of golf balls ordered by customers has the given probability distribution. . The probability distribution is discrete.3. The mean height and standard deviation of twenty5-year-old children are given.4. The significance level for the hypothesis test is0.01.

STEP 2

To find the probability of ordering at most2 golf balls, we need to sum the probabilities of ordering1 or2 golf balls.(x≤2)=(x=1)+(x=2)(x \leq2) =(x=1) +(x=2)(x≤2)=(x=1)+(x=2)

STEP 3

Plug in the given probabilities for ordering1 and2 golf balls to calculate the probability.(x≤2)=0.14+0.02(x \leq2) =0.14 +0.02(x≤2)=0.14+0.02

STEP 4

Calculate the probability of ordering at most2 golf balls.(x≤2)=0.14+0.02=0.16(x \leq2) =0.14 +0.02 =0.16(x≤2)=0.14+0.02=0.16

STEP 5

To find the probability of ordering at least one golf ball, we need to sum the probabilities of ordering1,2,3,4, or5 golf balls.(x≥1)=(x=1)+(x=2)+(x=3)+(x=4)+(x=5)(x \geq1) =(x=1) +(x=2) +(x=3) +(x=4) +(x=5)(x≥1)=(x=1)+(x=2)+(x=3)+(x=4)+(x=5)

STEP 6

Plug in the given probabilities for ordering1,2,3,4, and5 golf balls to calculate the probability.(x≥1)=0.14+0.02+0.36+0.38+0.10(x \geq1) =0.14 +0.02 +0.36 +0.38 +0.10(x≥1)=0.14+0.02+0.36+0.38+0.10

STEP 7

Calculate the probability of ordering at least one golf ball.(x≥1)=0.14+0.02+0.36+0.38+0.10=1(x \geq1) =0.14 +0.02 +0.36 +0.38 +0.10 =1(x≥1)=0.14+0.02+0.36+0.38+0.10=1

STEP 8

To find the mean, we need to multiply each value of x by its corresponding probability and sum these products.μ=∑x⋅(x)\mu = \sum x \cdot(x)μ=∑x⋅(x)

STEP 9

Plug in the given values for x and their corresponding probabilities to calculate the mean.μ=⋅.14+2⋅.02+3⋅.36+4⋅.38+5⋅.\mu =\cdot.14 +2\cdot.02 +3\cdot.36 +4\cdot.38 +5\cdot.μ=⋅.14+2⋅.02+3⋅.36+4⋅.38+5⋅.

STEP 10

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Assumptions1. The number of golf balls ordered by customers has the given probability distribution. . The probability distribution is discrete.
3. The mean height and standard deviation of twenty5-year-old children are given.
4. The significance level for the hypothesis test is0.01.

To find the probability of ordering at most2 golf balls, we need to sum the probabilities of ordering1 or2 golf balls.
$(x \leq2) =(x=1) +(x=2)$

Plug in the given probabilities for ordering1 and2 golf balls to calculate the probability.
$(x \leq2) =0.14 +0.02$

Calculate the probability of ordering at most2 golf balls.
$(x \leq2) =0.14 +0.02 =0.16$

To find the probability of ordering at least one golf ball, we need to sum the probabilities of ordering1,2,3,4, or5 golf balls.
$(x \geq1) =(x=1) +(x=2) +(x=3) +(x=4) +(x=5)$

Plug in the given probabilities for ordering1,2,3,4, and5 golf balls to calculate the probability.
$(x \geq1) =0.14 +0.02 +0.36 +0.38 +0.10$

Calculate the probability of ordering at least one golf ball.
$(x \geq1) =0.14 +0.02 +0.36 +0.38 +0.10 =1$

To find the mean, we need to multiply each value of x by its corresponding probability and sum these products.
$\mu = \sum x \cdot(x)$

Plug in the given values for x and their corresponding probabilities to calculate the mean.
$\mu =\cdot.14 +2\cdot.02 +3\cdot.36 +4\cdot.38 +5\cdot.$