Question

# A student takes a multiple choice test consisting of 5 questions where there are 4 choices...

A student takes a multiple choice test consisting of 5 questions where there are 4 choices per question. Also, each question is worth 20 points. Suppose the student guesses on each question. Let X be the number of questions the student gets correct. The probability distribution for X is given below. Find the variance of X. Do not give units and give your answer to four decimal places.

 x 0 1 2 3 4 5 P(X=x) 0.2373 0.3955 0.2637 0.0879 0.0146 0.001

Solution:

The formula for variance is given as below:

Variance = ∑ P(X)*(X - mean)^2

The calculation table is given as below:

 X P(X) XP(X) (X - mean)^2 P(X)*(X - mean)^2 0 0.2373 0 1.5625 0.37078125 1 0.3955 0.3955 0.0625 0.02471875 2 0.2637 0.5274 0.5625 0.14833125 3 0.0879 0.2637 3.0625 0.26919375 4 0.0146 0.0584 7.5625 0.1104125 5 0.001 0.005 14.0625 0.0140625 Total 1 1.25 0.9375

Variance = ∑ P(X)*(X - mean)^2

Variance = 0.9375

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