In the study of fingerprints, an important quantitative characteristic is the total ridge count for the 10 fingers of an individual. Suppose that the total ridge counts of individuals in a certain population are approximately normally distributed with a mean of 140 and a standard deviation of 50.

Find the probability that an individual picked at random from this population will have a ridge count of:

(a) 200 or more

(b) Less than 100

(c) Between 100 and 200

(d) Between 200 and 250

(e) In a population of 10,000 people how many would you expect to have a ridge count of 200 or more?