Consider the variable x=time required for a college student to complete a standardized exam. Suppose that for the population of students at a particular university, the distribution of x is well apprixmated by a normal curve with mean 45 min and standard deviation 5 min.
a. If 50 min is allowed for the exam, what proportion of student at this university would be unable to finish in the alloted time?
b. How much time should be allowed for the exam if we wanted 90 % of the students taking the test to be able to finish in the alloted time
c. How much time is required for the fastest 25 % of all students to complete the exam?