Problem 3) (Note that a) and b) are separate problems) a) In the spring each year, applicants to a certain college take a qualifying exam to determine their eligibility for admission to a special program. Only the top 33% of those taking the exam are eligible for admission. If the average score on the exam is 80 points with a standard deviation of 12 points, what is the minimum score that an applicant must make to be considered eligible? Round your answer to 2 decimal places. Show work. (7 points) b) Suppose that a random variable X has a continuous uniform distribution f(x) = 1/2 0 4x6 otherwise A random sample of size n = 49 is selected from this population. Find the probability that the sample mean is greater than 5.25. Round your answer to 4 decimal places. Show work. (7 points)