Use the following to answer the question(s) below.
A men's clothing store has determined the following probability distribution for the number of special size orders placed per month. The distribution is as follows:
Number Ordered Probability
0 0.10
5 0.10
10 0.12
15 0.30
20 0.38
-The standard deviation in the number of special size orders placed per month is
A) 24.516
B) 4.95
C) 15.345
D) 6.60
E) 3.88

Question

Quizplus · Accepted Answer

To find the standard deviation, we need to first find the mean (expected value) of the distribution:

Mean = (0)(0.10) + (5)(0.10) + (10)(0.12) + (15)(0.30) + (20)(0.38) 
= 2 + 1.2 + 4.5 + 7.6 
= 15.3

Using the formula for variance, we have:

Variance = [(0 - 15.3)^2(0.10) + (5 - 15.3)^2(0.10) + (10 - 15.3)^2(0.12) + (15 - 15.3)^2(0.30) + (20 - 15.3)^2(0.38)] 
= 73.674

Therefore, the standard deviation is the square root of the variance:

Standard deviation = sqrt(73.674) ≈ 6.60

So, the best choice is D.

Use the Following to Answer the Question(s) Below