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.)  b) What is the chance 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.)   c) Calculate the probability 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.)   d) How strange would it be to obtain a sample mean greater than 6.5 hours?  This is very unlikely.This is very likely.

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Asked Nov 4, 2019
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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.)

 

 

b) What is the chance 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.)

 

 

 

c) Calculate the probability 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.)

 

 

 

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

 

 

  • This is very unlikely.
  • This is very likely.

 

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Expert Answer

Step 1

Hey, since there is multiple subpart questions posted, we will answer first three subparts. If you want any specific subpart to be answered then please submit that subpart only or specify the subpart number in your message.

Step 2

Central Limit Theorem for mean:

If a random sample of size n is taken from a population having mean µ and standard deviation σ then, as the sample size increases, the sample mean approaches the normal distribution with mean µ  and standard deviation σ/ sqrt(n).

Step 3

a)Calculating the standard error of the mean:

Students spent an average of 5.5 hours per week playing organized sports. Random samples of 121 (n) studen...

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Standard error= Vn 2.2 121 2.2 11 0.2

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