A population has a mean of 50 and a standard deviation of 19. If a random sample of 64 is taken, what is the probability that the sample mean is each of the following?
a. Greater than 53
b. Less than 53
c. Less than 47
d. Between 47.5 and 51.5
e. Between 50.9 and 51.5
(Round the values of z to 2 decimal places. Round your answers to 4 decimal places.)