The mean annual automobile insurance premium is $950, with a standard deviation of $175. The data set has a bell-shaped distribution. Estimate the percent of premiums that are between $600 and $1300.

Question

Jillian Roman

Mathematics

11 August, 00:44

The mean annual automobile insurance premium is $950, with a standard deviation of $175. The data set has a bell-shaped distribution. Estimate the percent of premiums that are between $600 and $1300.

+2

Answers (1)

Know the Answer?

Jayleen Malone · Answer 1

95% of premiums that are between $600 and $1300.

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 = 950

Standard deviation = 175

Estimate the percent of premiums that are between $600 and $1300.

600 = 950 - 2*175

So 600 is two standard deviations below the mean.

1300 = 950 + 2*175

So 1300 is two standard deviations above the mean

By the Empirical Rule, 95% of premiums that are between $600 and $1300.