Question

The Polk Company reported that the average age of a car on U.S. roads in a recent year was 7.5 years. Suppose the distribution of ages of cars on U.S. roads is approximately bell-shaped. (a) If 99.7% of the ages are between 1 year and 14 years, what is the standard deviation of car age? (5 points) (b) Suppose

Answer 1

Answer:

The standard deviation of car age is 2.17 years.

Step-by-step explanation:

The Empirical Rule states that, for a normally distributed random variable:

68% of the measures are within 1 standard deviation of the mean.

95% of the measures are within 2 standard deviation of the mean.

99.7% of the measures are within 3 standard deviations of the mean.

In this problem, we have that:

Mean = 7.5

(a) If 99.7% of the ages are between 1 year and 14 years, what is the standard deviation of car age?

This means that 1 is 3 standard deviations below the mean and 14 is 3 standard deviations above the mean.

So

$14 = 7.5 + 3\sigma$

I want to find $\sigma$

$3\sigma = 6.5$

$\sigma = \frac{6.5}{3}$

$\sigma = 2.17$

The standard deviation of car age is 2.17 years.

Answer 2

Answer:

2.167

Step-by-step explanation:

We know that 99.7% of the data are within 3 standard deviations of the mean = 6.5 years ( I found that from 14 - 7.5 or 7.5 - 1). So 6.5/3 = 2.167.