Professor Sanchez has been teaching Principles of Economics for over 25 years. He uses the following scale for grading.



Grade Numerical Score Probability
A 4 0.120
B 3 0.210
C 2 0.400
D 1 0.155
F 0 0.115

a. Convert the above probability distribution to a cumulative probability distribution. (Round your answers to 3 decimal places.)

b. What is the probability of earning at least a B in Professor Sanchez’s course? (Round your answer to 3 decimal places.)

c. What is the probability of passing Professor Sanchez’s course? (Round your answer to 3 decimal places.)

1 answer

a. To convert the probability distribution to a cumulative probability distribution, we need to add up the probabilities for each grade up to that point.

Grade Numerical Score Probability Cumulative Probability
A 4 0.120 0.120
B 3 0.210 0.120 + 0.210 = 0.330
C 2 0.400 0.330 + 0.400 = 0.730
D 1 0.155 0.730 + 0.155 = 0.885
F 0 0.115 0.885 + 0.115 = 1.000

b. The probability of earning at least a B is the cumulative probability for a B or higher. From the table in part a, the cumulative probability for a B is 0.330. Therefore, the probability of earning at least a B is 0.330.

c. The probability of passing the course is the cumulative probability for a C or higher. From the table in part a, the cumulative probability for a C is 0.730. Therefore, the probability of passing the course is 0.730.