Question

A random variable is normally distributed, with a mean of 14 and a standard deviation of 3. (a) If you take a sample of size 10, what can you say about the shape of the sampling distribution of the sample mean? Why? (b) For a sample of size 10, state the mean and standard deviation of the sampling distribution of the sample mean. (c) Suppose it turns out that the original distribution (the original random variable) IS NOT EVEN CLOSE TO BEING NORMAL. If you NOW take a sample of size 35, what can you say about the shape of the sampling distribution of the sample mean? Why? (d) For a sample of size 35, state the mean and the standard deviation of the sampling distribution of the sample mean.

Answer 1

µ = 14

sd = 3

a) Shape of sampling distribution is bell shaped. Because the original distribution is normal distribution.

b) Mean of sampling distribution = µ = 14

Standard deviation of sampling distribution = sd / sqrt(n) = 3 / sqrt(10) = 0.95

c) n = 35

Shape of sampling distribution is bell shaped. Because of central limit theorem and n is greater than 30.

d) Mean of sampling distribution = µ = 14

Standard deviation of sampling distribution = sd / sqrt(n) = 3 / sqrt(35) = 0.51