At the Department of Education at UR University student records suggest that the

Question

At the Department of Education at UR University student records suggest that the population of students spends an average of 5.5 hours per week playing organized sports. The population’s standard deviation is 2.2 hours per week. Based on a sample of 121 students, Healthy Lifestyles Incorporated (HLI) would like to apply the central limit theorem to make various statements.

a. Compute the standard error of the sample mean.
b. What is the chance that HLI will find a sample mean between 5 and 6 hours?
c. Calculate the probability that the sample mean will be between 5.3 and 5.7 hours.
d. How strange would it be to obtain a sample mean greater than 6.5 hours?

Explanation / Answer

In the department of education at UR university, student records suggest that the population of students spends an average of 5.5 hrs per week playing organized sports. The population's standard deviation is 2.2 hrs per week.
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Based on a sample of 121 students, healthy lifestyles Inc.
(HLI) would like to apply the central limit theorem to make various estimates.
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Compute the standard error of the sample mean?
Ans: 2.2/sqrt(121) = 0.2
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What is the chance HLI will find a sample mean between 5 and 6 hrs?
t(5) = (5-5.5)/0.2 = -2.5

t(6) = (6-5.5)/0.2 = +2.5
P(5< x-bar <6) = P(-2.5< t < 2.5 when df=120) = 0.9862
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Calculate the probability that the sample mean will be between 5.3 and 5.7 hrs
how strange would it be to obtain a sample mean greater than 6.5 hrs?
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Find the t-values; then find the probabilities.

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