Question: An actuary is a financial expert who applies mathematical and statistical methods to assess financial and other risks relating to various contingent events and then arrives at the rate or premium that a person should pay to get a particular insurance coverage. There is an acute shortage of qualified actuaries so that only 30% of the people who do the job worldwide are qualified, with some consequences. If a survey of 400 people who do the job of an actuary are surveyed, what is the probability that the proportion who are qualified: (a) exceeds 0.24? (b) is between 0.26 and 0.36? (c) is less than 0.35?