Question

The standard deviation of X is 0.9. Which of the following is the best interpretation of this value?

a. About 90% of subjects solved 3 or fewer puzzles.

b. About 68% of subjects solved between 0.9 puzzles less and 0.9 puzzles more than the mean.

c. The typical subject solved an average of 0.9 puzzles.

d. The number of puzzles solved by subjects typically differed from the mean by about 0.9 puzzles.

e. The number of puzzles solved by subjects typically differed from one another by about 0.9 puzzles.

Short answer

(d) The number of puzzles solved by subjects typically differed from the mean by about 0.9 puzzles.

Step-by-step solution

Given Information 

The standard deviation of X is 0.9.

X = The number of puzzles solved by a subject chosen at random

X's probability distribution is shown below.

Value	1	2	3	4
Probability	0.2	0.4	0.3	0.1

X's standard deviation is 0.9

Explanation for correct option 

The standard deviation is a measure of how far the variables deviate from the mean.

If the standard deviation is close to zero, the majority of the data is clustered around the mean, whereas if it is high, the data is dispersed.

The standard deviation in this case is 0.9, indicating that X (number of puzzles) deviates from the mean by 0.9 on average.

Step 3  / 3Step 3: Explanation for incorrect option

a. The standard deviation will not be 3 puzzles

b. The d standard deviation of will not be 0.9 puzzles less or greater

c. The standard deviation of will not be average of 0.9 puzzles

e. The standard deviation of will not be 0.9 puzzles