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...

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. 

a. What is the probability that the sample of ball bearings will have a mean less than 0.798cm?

b. What is the probability that the sample of ball bearings will have a mean of at least 0.815 cm?

c. What is the probability that the sample of ball bearings will have a mean between 0.798 and 0.815 cm?

d. For samples of size 36, 15% of all sample means are at most what diameter?