Question

Whereas grading students’ homework is an important aspect of a professor’s job, reviewing homework solutions is an important ingredient in the learning process for a student. Research indicates that the longer it takes a professor to grade a homework the less likely that a student will review the homework solutions, when made available. In the past, in Professor Johnson PHYS 500 class, nonadherence on part of a few students to a prescribed HW submission format has often delayed the turnaround time for posting homework grades. In fact, in a few cases, homework’s were left ungraded till the end of the semester. Concerned about the impact this would have on student learning, the professor regularly reminded the students about the submission format, which yielded marginal positive results. Note that the time taken by the professor to grade a student's homework is normally distributed with a mean of 12.6 minutes and a standard deviation of 2.5 minutes.

1. What is the probability that a randomly selected homework will require less than 16 minutes to grade?
2. What is the probability that randomly selected homework will require more than 12 minutes to grade?
3. What is the probability that randomly selected homework will require between 11 and 15 minutes to grade?

Answer 1

Let "X" be time taken by the professor to grade a student's homework

Refer Z-table to find the probability or use excel formula "=NORM.S.DIST(1.36, TRUE)" to find the probability.

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Refer Z-table to find the probability or use excel formula "=NORM.S.DIST(-0.24, TRUE)" to find the probability.

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Refer Z-table to find the probability or use excel formula "=NORM.S.DIST(-0.64, TRUE)" & "=NORM.S.DIST(0.96, TRUE)" to find the probability.