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 5.5 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 estimates.

a. Compute the standard error of the sample mean. (Round your answer to 1 decimal place.)

Standard error ______

b. What is the chancce HLI will find a sample mean between 5 and 6 hours? ( Round Z value to 2 decimal places. Round your answer to 4 decimal places.)

Chance______

c. Calculate the probabiltiy that the sample mean will be between 5.3 and 5.7 hours. (Round z value to 2 decimal places. Round your answer to 4 decimal places.)

Probabiltiy _____

d. How strange would it be to obtain a sample mean greater than 6.5 hours?

- This is very unlikely

0r, is this very likely

Explanation / Answer

A)Standred error =2.2/start (121)=0.2

B) 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 ) = 0.986

C)t(5) = (5.3-5.5)/0.2 = -1
t(6) = (5.7-5.5)/0.2 = +1
P(5< x-bar <6) = P(-1< t < +1) =  0.6827

D)p(more than 6.5)=

P(6.5-5.5)/0.2= p(5)=0.00000029

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