# A variable of a population has a mean of µ = 35 and a standard deviation of σ = 42.a. If the variable is normally distributed, identify the sampling distribution of the sample mean for samples of size 9.b. Can you answer part (a) if the distribution of the variable under consideration is unknown? Explain your answer.c. Can you answer part (a) if the distribution of the variable under consideration is unknown but the sample size is 36 instead of 9? Why or why not?

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A variable of a population has a mean of µ = 35 and a standard deviation of σ = 42.

a. If the variable is normally distributed, identify the sampling distribution of the sample mean for samples of size 9.
b. Can you answer part (a) if the distribution of the variable under consideration is unknown? Explain your answer.
c. Can you answer part (a) if the distribution of the variable under consideration is unknown but the sample size is 36 instead of 9? Why or why not?

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Step 1

a.

Sampling distribution of a sample mean:

Step 2

The mean value is,

Step 3

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