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 of 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 calculate the standard deviation of a probability distribution, we need to first calculate the expected value (mean) of the distribution.

Expected value = (0)(0.10) + (5)(0.10) + (10)(0.12) + (15)(0.30) + (20)(0.38)

Expected value = 14

Next, we need to calculate the variance, which is the sum of the squared deviation from the mean, multiplied by the probability, for each value.

Variance = [(0 - 14)^2(0.10) + (5 - 14)^2(0.10) + (10 - 14)^2(0.12) + (15 - 14)^2(0.30) + (20 - 14)^2(0.38)]

Variance = 123.56

Finally, we can calculate the standard deviation by taking the square root of the variance.

Standard deviation = √123.56

Standard deviation = 6.60

Therefore, the correct answer is D) 6.60.

Use the Following to Answer the Question(s) Below