To estimate the mean height μ of male students on your campus,
you will measure an SRS of students. Heights of people of the same
sex and similar ages are close to Normal. You know from government
data that the standard deviation of the heights of young men is
about 2.8 inches. Suppose that (unknown to you) the mean height of
all male students is 70 inches.
(a) If you choose one student at random, what is the probability
that he is between 67 and 70 inches tall?
(b) You measure 25 students. What is the standard deviation of
the sampling distribution of their average height x¯¯¯?
(c) What is the probability that the mean height of your sample
is between 67 and 70 inches?