A Sample of Size 400 Is Drawn from a Population $\bar { X }$

Essay

A sample of size 400 is drawn from a population whose mean and variance are 5000 and 10 000, respectively. Find the following probabilities.
a. P( $\bar { X }$ < 4,990).
b. P(4995 < $\bar { X }$ < 5010).
c. P( $\bar { X }$ = 5000).