For a population with m 50 and s 6 describe the shape the

For a population with m = 50 and s = 6, describe the shape, the mean, and the standard deviation for the distribution of sample means for each of the following:
a. Samples of n = 4.
b. Samples of n = 36.

Solution

A)

The mean of any sampling distribution is the same as the mean of the original distribution, so

Mean = 50 [answer]

Meanwhile, the standard deviation is

SE = s/sqrt(n) = 6/sqrt(4) = 3 [answer]

Now, the the shape, according to the central limit theorem, will be bell shaped, like the normal distribution.

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B)

The mean of any sampling distribution is the same as the mean of the original distribution, so

Mean = 50 [answer]

Meanwhile, the standard deviation is

SE = s/sqrt(n) = 6/sqrt(36) = 1 [answer]

Now, the the shape, according to the central limit theorem, will be bell shaped, like the normal distribution.