Question

8. I have done a review of grades in my classes over the past few years. I have noticed that final grades follow a distribution similar to the one below:

Grade Probability

A 15%

B 30%

C 35%

D 10%

F 10%

Do a Monte Carlo simulation for the next 10 students. How many students earned a B? Use the following random # stream. (21 00 52 87 15 42 17 76 35 76 98 32 65)

Answer 1

six students earned grade B.

Answer 2

To perform a Monte Carlo simulation for the next 10 students and determine how many students earned a B, we will use the given probabilities and the provided random number stream.

The random number stream is: (21 00 52 87 15 42 17 76 35 76 98 32 65)

1. Assign probabilities to each grade:

Grade A: 15% Grade B: 30% Grade C: 35% Grade D: 10% Grade F: 10%

2. Generate grades for the next 10 students using the random number stream:

For each random number from the stream, we will compare it to the cumulative probabilities to determine the grade for each student.

Let's walk through the simulation step by step:

Student 1: Random number = 21

Cumulative Probability A: 0.15 Cumulative Probability B: 0.45 (0.15 + 0.30) Cumulative Probability C: 0.80 (0.15 + 0.30 + 0.35)

Since the random number 21 falls between 0 and 0.15, the student earns a Grade A.

Student 2: Random number = 00

The random number 00 falls between 0 and 0.15, so the student earns a Grade A.

Student 3: Random number = 52

Cumulative Probability A: 0.15 Cumulative Probability B: 0.45 (0.15 + 0.30) Cumulative Probability C: 0.80 (0.15 + 0.30 + 0.35)

Since the random number 52 falls between 0.45 and 0.80, the student earns a Grade C.

Student 4: Random number = 87

Cumulative Probability A: 0.15 Cumulative Probability B: 0.45 (0.15 + 0.30) Cumulative Probability C: 0.80 (0.15 + 0.30 + 0.35)

Since the random number 87 falls between 0.80 and 1.00, the student earns a Grade F.

Student 5: Random number = 15

The random number 15 falls between 0 and 0.15, so the student earns a Grade A.

Student 6: Random number = 42

Cumulative Probability A: 0.15 Cumulative Probability B: 0.45 (0.15 + 0.30) Cumulative Probability C: 0.80 (0.15 + 0.30 + 0.35)

Since the random number 42 falls between 0.15 and 0.45, the student earns a Grade B.

Student 7: Random number = 17

The random number 17 falls between 0 and 0.15, so the student earns a Grade A.

Student 8: Random number = 76

Cumulative Probability A: 0.15 Cumulative Probability B: 0.45 (0.15 + 0.30) Cumulative Probability C: 0.80 (0.15 + 0.30 + 0.35)

Since the random number 76 falls between 0.45 and 0.80, the student earns a Grade C.

Student 9: Random number = 35

Cumulative Probability A: 0.15 Cumulative Probability B: 0.45 (0.15 + 0.30) Cumulative Probability C: 0.80 (0.15 + 0.30 + 0.35)

Since the random number 35 falls between 0.15 and 0.45, the student earns a Grade B.

Student 10: Random number = 76

Cumulative Probability A: 0.15 Cumulative Probability B: 0.45 (0.15 + 0.30) Cumulative Probability C: 0.80 (0.15 + 0.30 + 0.35)

Since the random number 76 falls between 0.45 and 0.80, the student earns a Grade C.

In summary, among the 10 students, 2 students earned a Grade B.