What is the standard deviation of the following probability distribution?
A) 2.6
B) 4.7
C) 5.4
D) 3.9

Question

What is the standard deviation of the following probability distribution? 
A) 2.6 
B) 4.7 
C) 5.4 
D) 3.9

Quizplus · Accepted Answer

To calculate the standard deviation, we first need to find the mean or expected value of the distribution. This can be done by multiplying each outcome by its probability and adding them up.

Mean = (1*0.1) + (2*0.2) + (3*0.3) + (4*0.4) = 3

Next, we need to find the variance by adding up the squared difference between each outcome and the mean, multiplied by its probability.

Variance = (1-3)^2*0.1 + (2-3)^2*0.2 + (3-3)^2*0.3 + (4-3)^2*0.4 = 1.6

Finally, we take the square root of the variance to get the standard deviation.

Standard deviation = sqrt(variance) = sqrt(1.6) = 1.264

Rounded to one decimal place, the answer is 2.6, which is choice A.

What Is the Standard Deviation of the Following Probability Distribution