Question

During the registration period at a college, the Dean prepares a daily enrollment report to monitor student enrollments in classes. The amount of time it takes to prepare an enrollment report is uniformly distributed between 4 and 12 minutes. Find the probability it will take at least 10 minutes to prepare the enrollment report.

Answer 1

During the registration period at a college, the Dean prepares a daily enrollment report to monitor student enrollment in classes.

The amount of time it takes to prepare an enrollment report is uniformly distributed between 4 and 12 minutes.

We have to find the probability that it will take at least 10 minutes to prepare the enrollment report.

Now, if X be the time required to prepare a randomly selected daily report, then X follows Uniform distribution between 4 and 12.

So, the PDF of X is given by

Now, we have to find

So, the required probability is 0.25.