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Mean of Sampling Distribution

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The assets (in billions of dollars) of the four wealthiest people in a particular country are 47,35,28,11. Assume that the sample of size 2 are randomly selected with replacement from this population of four values.

a) After listing the possible samples and finding the mean of each sample, use the table to describe the sampling distribution of the sample means.

x ? Probability

47 _____
41 _____
37.5 _____
35 _____
31.5 _____
29 _____
28 _____
23 _____
19.5 ____
11 ____

b). Find the mean of the sampling distribution
µ =____( Please round to two decimal places as needed)

c). Is the mean of the sampling distribution [from part (b) equal to the mean of the population of the four listed values, if so are those means always equal. Why or why not.

Solution Summary

The solution determines the mean of the sampling distribution.

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The assets (in billions of dollars) of the four wealthiest people in a particular country are 47,35,28,11. Assume that the sample of size 2 are randomly selected with replacement from this population of four values
a) After listing the possible samples and finding the mean of each sample, use ...

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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!"
• "Thank you"
• "Thank you very much for your valuable time and assistance!"

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