4. An international development bank is looking for candidates for its Young Professionals Program. In past recruitment periods, 45 percent of the applicants had doctoral degrees. For a randomly selected

sample of 21 applicants, the discrete variable x being the number of applicants with doctoral degrees in the sample. a. Calculate the mean and the standard deviation of the binomial distribution. b. Using the binomial probability formula, solve for the probability that x = 10. c. Repeat part (b), this time using the normal approximation to the binomial. d. Using the normal distribution to approximate the binomial, find the probability that no more than 9 people in the sample have doctoral degrees.