Question

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	.0010

Answer 1

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