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

To calculate the standard deviation, we first need to find the mean of the distribution:

μ = Σ(xi * P(xi)) = (0*0.1)+(1*0.3)+(2*0.2)+(3*0.2)+(4*0.1)+(5*0.1) = 2.2

Next, we can calculate the variance using the formula:
σ^2 = Σ(xi - μ)^2 * P(xi)
= ((0-2.2)^2*0.1)+((1-2.2)^2*0.3)+((2-2.2)^2*0.2)+((3-2.2)^2*0.2)+((4-2.2)^2*0.1)+((5-2.2)^2*0.1)
= 1.96

Finally, we can find the standard deviation by taking the square root of the variance:
σ = √1.96 ≈ 2.49

Therefore, the answer is B) 2.49.

Below Is the Probability Distribution for Random Variable X