Chapter 6.1, Problem 32E

To determine

To Explain: the best interpretation of the value 1.08

Answer to Problem 32E

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

Explanation of Solution

Given:

Number of cars	0	1	2	3	4	5
Probability	0.09	0.36	0.35	0.13	0.05	0.02

  ${\sigma }_X=1.08$

1. Incorrect, because 1.08 corresponds to standard deviation
2. Correct, because Standard deviation is 1.08 and mean is 1.75 so the number of cars varies about 1.08 from the mean 1.75
3. Incorrect, because data values would be vary about 1.08 standard deviation from the mean 1.75, so it possible that number of cars to be more than one.
4. Incorrect, because 68% follows the empirical rule, but it can only use the empirical rule, the approximately of population distribution is normal distribution; in this case don’t know the population distribution.
5. Incorrect, the mean is the expected value and therefore there is no point to saying that the mean by itself is about 1.08.

Hence, the correct option is (b)