# statistic problems (2) must show details

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**5.17 **

Suppose a random sample of n measurements is selected from a population with mean u = 100 and variance o2 = 100. For each of the following values of n, give the mean and standard deviation of the sampling distribution of the sample mean x.

a.n = 4

b.n = 25

c.n = 100

d.n = 50

e.n = 500

f.n = 1,000

**5.18**

A random sample of n = 64 observations is drawn from a population with a mean equal to 20 and a standard deviation equal to 16.

a.Give the mean and standard deviation of the (repeated) sampling distribution of x.

b.Describe the shape of the sampling distribution of x. Does your answer depend on the sample size?

c.Calculate the standard normal z- score corresponding to a value of x = 15.5

d.Calculate the standard normal z – score corresponding to x = 23.

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