Based on all student records at Camford University, students spend an average of

Question

Based on all student records at Camford University, students spend an average of 5.20 hours per week playing organized sports.The populations standard deviation is 3.40 hours per week. Based on a sample of 81 students, Healthy Lifestyles Incorporated would like to apply the central limit theorem to make various estimates.

A. Compute the standard deviation of the mean (round to 2 decimal places)

B. What is the chance HLI will find a sample mean between 4.5 and 5.9 hours? ( round your z and standard error values to 2 decimal places and final answer to 4 decimal places)

C. Calculate the proability that the sample mean will be between 4.8 and 5.6 hours. ( round your z and standard error values to 2 decimal places and final answer to 4 decimal places)

D. How strange would it be to obtain a sample mean greated than 7.70 hours?

1. This is very likely 2. This is very unlikely

Explanation / Answer

(a) SE = 3.4/sqrt 81 = 0.38


(b) z1 = (4.5-5.2)/0.38 = -1.84, z2 = (5.9-5.2)/0.38 = 1.84,
P(-1.84 < z < 1.84) = 0.9342

c) z1 = (4.8-5.2)/0.38 = -1.05, z2 = (5.6-5.2)/0.38 = 1.05,
P(-1.05 < z < 1.05) = 0.7062

d) z =(7.7-5.2)/0.38 = 6.57

P(6.57) =0

So it is 2. This is very unlikely

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