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.
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