Problem:
An instructor allows students to take an exam as many times as needed until the student obtains a passing grade. The following is a record of the number of students in a class of 20 who took the test and the number of tests taken in order to obtain a passing grade.
| Students |
Number of Tests |
| 9 |
1 |
| 6 |
2 |
| 3 |
3 |
| 2 |
4 |
Required:
Question 1) Use the relative frequency approach to construct a probability distribution and show that it satisfies the required condition.
Question 2) Find the expected value of the number of tests taken.
Question 3) Compute the variance.
Question 4) Compute the standard deviation.
Solve the given numerical problem and illustrate step by step calculation.