In a study of fingerprints an important measure is the total ridge count for the 10 fingers of an individual. Suppose that the total ridge count for the Australian adult male population are normally distributed with a mean of 140 and a variance of 2500. LetX

Xdenote the total ridge count of a randomly selected individual from the Australian adult male population

a.What is the probability that a randomly selected individual will have atotal ridge countof at least 200

b.Thetotal ridge countfor a randomly selected individual falls at the 74.54th percentile. What is thetotal ridge countfor this individual

c.LetXdenote the meantotal ridge countof 50 individuals randomly selected from the Australian adult male population. What is the distribution ofXin conventional statistical notation