Find the expected value of the number of tests taken. b. Compute the variance an

Question

Find the expected value of the number of tests taken.

b. Compute the variance and the standard deviation of the number of tests taken.

S. A calculus instmctor uses computer aided instruction and ailows students to tak,e the midterm exam as many times as needed until a passing grade is obtained. Following is a record of the number of students in a class of 40 who took the test each number of times Students Number of Tests 20 10 4 a. Find the expected value of the number of tests taken. (10 points) Compute the variance and the standard deviation of the number of tests taken. (10 points) b.

Explanation / Answer

Student(f) Number of test taken(x) x*f (x-mean)^2 f*(x-mean)^2 20 1 20 0.680625 13.6125 10 2 20 0.030625 0.30625 7 3 21 1.380625 9.664375 3 4 12 4.730625 14.191875 Total 40 73 37.775 Mean = sum(f*x)/sum(f) = 73/40 = 1.825 Variance = 37.775/40 = 0.944375 Standard deviation = sqrt(0.944375) = 0.97178

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