Question

Exercises 31–33 refer to the following setting. Choose an American household at random and

let the random variable X be the number of cars (including SUVs and light trucks) they own.

Here is the probability distribution if we ignore the few households that own more than 5cars

The standard deviation of X is $\sigma X=1.08$. If many households were selected at random, which of the following would be the best interpretation of the value 1.08?

a. The mean number of cars would be about 1.08.

b. The number of cars would typically be about 1.08 from the mean.

c. The number of cars would be at most 1.08 from the mean.

d. The number of cars would be within 1.08 from the mean about 68% of the time.

e. The mean number of cars would be about 1.08 from the expected value.

Short answer

(b) is the best interpretation of the value 1.08 .

Step-by-step solution

Step 1. Given information  

We have given probability distribution:

Step 2. To find the the best interpretation of the value 1.08?  

a. The mean number of cars would be about 1.08.

b. The number of cars would typically be about 1.08 from the mean.

c. The number of cars would be at most 1.08 from the mean.

d. The number of cars would be within 1.08 from the mean about 68% of the time.

e. The mean number of cars would be about 1.08 from the expected value.

From above statements we conclude that (b) is correct and thus (b) is the best interpretation.