Question

The lifespans of meerkats in a particular zoo are normally distributed. The average meerkat lives 10.4

years; the standard deviation is 1.9 years.

arzo

Use the empirical rule (68 - 95 - 99.7%) to estimate the probability of a meerkat living between 12.3

and 14.2 years

PLEASE HELP

Answer 1

13.5% probability of a meerkat living between 12.3 and 14.2 years.

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 = 10.4

Standard deviation = 1.9

The normal distribution is symmetric, which means that 50% of the measures are below the mean and 50% are above the mean.

Between 12.3 and 14.2 years.

12.3 = 10.4 + 1.9

So 12.3 is one standard deviation above the mean.

50% of the measures are above the mean. Of those, 68% are within 1 standard deviation of the mean.

14.2 = 10.4 + 2*1.9

So 14.2 is two standard deviations above the mean.

50% of the measures are above the mean. Of those, 95% are within 2 standard deviation of the mean.

0.5*0.95 - 0.5*0.68 = 0.135

13.5% probability of a meerkat living between 12.3 and 14.2 years.