Below is the probability distribution for random variable x.What is the standard deviation of this probability distribution?

A) 6.20
B) 2.49
C) 1.00
D) 0.35

Question

Below is the probability distribution for random variable x.What is the standard deviation of this probability distribution?

A) 6.20 
B) 2.49 
C) 1.00 
D) 0.35

Quizplus · Accepted Answer

The formula for standard deviation of a probability distribution is: 
SD = sqrt(variance), where variance = E[(X-E[X])^2]
Using the formula and the given probability distribution, we get:
E[X] = (2)(0.2) + (4)(0.4) + (6)(0.3) + (8)(0.1) = 4.6
Variance = [(2-4.6)^2(0.2) + (4-4.6)^2(0.4) + (6-4.6)^2(0.3) + (8-4.6)^2(0.1)] = 4.94
Standard deviation = sqrt(4.94) = 2.49 (rounded to two decimal places). Therefore, the best choice is B.

Below Is the Probability Distribution for Random Variable X