The mean diameter of a ball bearing produced by a certain manufacturer is 0.80 cm with a standard deviation of 0.03 cm. A sample of 36 ball bearings is randomly selected from a production run. Answer the following:
a) What is the probability that the sample of balls bearings will have a mean less than .798 cm?
b) What is the probability that the sample of ball bearings will have a mean of at least .815 cm?
c) What is the probability that the sample of ball bearings will have a mean between .798 and .815 cm?
d) For samples of size 36, 15% of all sample means are at most what diameter?