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1. Random samples of size 15 are repeatedly drawn from a distribution that can be approximated...

1. Random samples of size 15 are repeatedly drawn from a distribution that can be approximated by a normal distribution with a mean of 65 and a standard deviation of 17. Since the values in the sample are random variables, the mean associated to those samples, ?̅, is also a random variable.

a. What is the expected mean of the distribution of ?̅?

b. What is the expected standard deviation of the distribution of ?̅?

Hi Chegg Answerer, could you, if possible, answer part b without using the central limit theorem? Thank you!

Math   Statistics-And-Probability   
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Answer #1

Solution :

mean = = 65

standard deviation = = 17

n = 15

The distribution of ?̅ is normal, because n is smaller than 30

a) =   = 65

b) = / n = 17 / 15 = 4.39

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