Question: A calculus instructor uses computer aided instruction and allows students to take the midterm as many times as needed until a passing grade is obtained. Following is a record of the percentage of students who took the test each number of times

Relative frequency Num ber of t est s

.5 1

.35 2

.1 3

.05 4

1. Show that the probability distribution satisfies the required condition
2. Find the expected value of the number of tests taken
3. Compute the variance
4. Compute the standard deviation

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