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 |
- Use the relative frequency approach to construct a probability distribution and show that it satisfies the required condition.
- Find the expected value of the number of tests taken.
- Compute the variance.
- Compute the standard deviation.