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 approximated by a normal distribution with mean 45 minutes and standard deviation 5 minutes.
a. If 50 minutes is allowed for the exam, what proportion of students at this university would be unable to finish in the allotted 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 allotted time?
c. How much time is required for the fastest 25% of all students to complete the exam?