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. Use Excel to answer the following questions.
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?