A random variable is normally distributed. It has a mean of 245 and a standard deviation of 21.
A random variable is normally distributed. It has a mean of 245 and a standard deviation of 21.
(a) Suppose we take a random sample of size 10.
(i) What is the shape of the distribution of the sample means? Why?
(ii) What is the mean of the sample means, and what is standard deviation of the sample means?
(iii) Find the probability that a sample mean is more than 241.
(b) Suppose we take a random sample of size 35.
(i) What is the shape of the distribution of the sample means? Why?
(ii) What is the mean of the sample means, and what is standard deviation of the sample means?
(iii) Find the probability that a sample mean is more than 241.
(c) Compare your answers in (a)(iii) and (b)(iii). Why is one smaller than the other?
