The mean diameter of a ball bearing produced by a certain manufacturer is 0.80cm with a standard deviation of 0.03cm. 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 0.798 cm?
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?