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 find the standard deviation, we first need to find the mean. 
Mean = (0.2*2 + 0.4*4 + 0.3*5 + 0.1*6) = 3.8

Next, we find the variance: 
Variance = (0.2*(2-3.8)^2 + 0.4*(4-3.8)^2 + 0.3*(5-3.8)^2 + 0.1*(6-3.8)^2) 
= 0.0976 + 0.0064 + 0.0189 + 0.0516 
= 0.1745

Finally, we take the square root of the variance to get the standard deviation: 
Standard deviation = √(0.1745)  ≈  0.24

Therefore, the best choice is B)2.49, which rounds to the nearest hundredth.

Below Is the Probability Distribution for Random Variable X