Question

The time taken by a professor to grade a student’s take home final exam in Organizational Behavior is uniformly distributed between 30 to 60 minutes. Let X be the time taken to grade a student’s final exam in Org Behavior. [Be sure to show your calculations.]

a. Draw the probability distribution of X.

b. What is the probability it will take less than 20 minutes to grade a student’s exam?

c. What is the expected value of grading time for a student?

d. What is the standard deviation of grading time for a student?

e. What is the probability that it will take between 40 and 50 minutes to grade a student’s exam?

f. In some semester, the professor has only 10 students in his class. He starts grading at 8AM. There is a show in the evening that he would like to attend. What is the likelihood that he will finish grading all his final exams by 5PM to leave in time for the show?

g. Does X obey the empirical rule? Justify briefly.

Answer #1

A large statistics class consists of 250 students. On the final
exam, the professor worries that question 13 might be unfair. He
resolves to drop question 13 if less than 40% of the class
correctly answers the question. After grading 125 randomly selected
final exams (out of 250 taken), a student calls the professor and
asks if question 13 will be dropped. The professor looks at the
graded exams and notes that 46 of the 125 graded exams got question...

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activity, watching cat videos. Fifteen students per hour arrive at
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minutes per student. If the average cat video is 60 seconds, how
many videos can the professor watch in an hour? A. 20 B. 18 C. 15
D. 24

Professor Elderman has given the same multiple-choice final exam
in his Principles of Microeconomics class for many years. After
examining his records from the past 10 years, he finds that the
scores have a mean of 76 and a standard deviation of 12.
What is the probability Professor Elderman’s class of 36 has a
class average below 78?
0.5675
0.1587
0.8413
Cannot be determined.

Suppose time taken to grade an exam-paper by an examiner has
mean 13.1 min. and standard deviation 6.1 min. If the examiner has
to grade 46 exam-papers, what is the approximate probability that
she will finish grading in less than 648 min. (assuming grading
times are independent and she grades continuously)? Answer to 4
decimal places.
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9. Suppose that the time that it takes a student to
complete this test is normally distributed. The mean time is 58
minutes with a standard deviation of 11 minutes. Use the empirical
rule to solve the following questions. Answers using the normal
calculator and not the empirical rule will be marked as
wrong.
a. What is the probability that a person will take
between 47 and 58 minutes? (Draw a picture to show your
answer.)
b. What is the...

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