# Sampling Distribution

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NBA salaries averaged 2.1 million with a standard deviation of 1.2 million in 2000. Suppose a sample of 36 NBA players was taken. A. What is the sampling distribution of the sample mean? aa) Approximately N(2.1, 1.2) (unit in millions) bb)Approximately N(1.2, 2.1) cc) Approximately N(2.1, .2) dd) Approximately N(1.2, .35) B. What is the approximate probability that the average salary of the 36 players exceeded $2.1 million? aa) .5 bb)36.0 cc) 0.00 dd) 1.80 Please show or explain how you derived at your solution and add any comments that you think will be helpful.

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NBA salaries averaged 2.1 million with a standard deviation of 1.2 million in 2000. Suppose a sample of 36 NBA players was taken. A. What is the sampling distribution of the sample mean? aa) Approximately N(2.1, 1.2) (unit in millions) bb)Approximately N(1.2, 2.1) cc) Approximately N(2.1, .2) dd) Approximately N(1.2, .35) B. What is the approximate probability that the average salary of the 36 players exceeded $2.1 million? aa) .5 bb)36.0 cc) 0.00 dd) 1.80 Please show or explain how you derived at your solution and add any comments that you think will be helpful.

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Solution. The answer for the first question is c) Appr. N(2.1,0.2) which means the mean is 2.1 million and the standard deviation is 0.2 ...

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- BSc , Wuhan Univ. China
- MA, Shandong Univ.

###### Recent Feedback

- "Your solution, looks excellent. I recognize things from previous chapters. I have seen the standard deviation formula you used to get 5.154. I do understand the Central Limit Theorem needs the sample size (n) to be greater than 30, we have 100. I do understand the sample mean(s) of the population will follow a normal distribution, and that CLT states the sample mean of population is the population (mean), we have 143.74. But when and WHY do we use the standard deviation formula where you got 5.154. WHEN & Why use standard deviation of the sample mean. I don't understand, why don't we simply use the "100" I understand that standard deviation is the square root of variance. I do understand that the variance is the square of the differences of each sample data value minus the mean. But somehow, why not use 100, why use standard deviation of sample mean? Please help explain."
- "excellent work"
- "Thank you so much for all of your help!!! I will be posting another assignment. Please let me know (once posted), if the credits I'm offering is enough or you ! Thanks again!"
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