Question

The lifespans of meerkats in a particular zoo are normally distributed. The average meerkat lives 10. 410. 410, point, 4 years; the standard deviation is 1. 91. 91, point, 9 years.

Use the empirical rule (68-95-99. 7\%)(68−95−99. 7%)left parenthesis, 68, minus, 95, minus, 99, point, 7, percent, right parenthesis to estimate the probability of a meerkat living less than 16. 116. 116, point, 1 years

Answer 1

To use the empirical rule, we first need to standardize the value of 16.1 using the formula:

z = (x - mu) / sigma

where x is the value we want to standardize, mu is the mean, and sigma is the standard deviation.

z = (16.1 - 10.4) / 1.91

z = 2.99

Now, we can use the empirical rule to estimate the probability:

About 68% of meerkats have lifespans within one standard deviation of the mean. This means that about 34% have lifespans less than 10.4 + 1.91 = 12.31 years.

About 95% of meerkats have lifespans within two standard deviations of the mean. This means that about 47.5% have lifespans less than 10.4 + 2 * 1.91 = 14.22 years.

About 99.7% of meerkats have lifespans within three standard deviations of the mean. This means that about 49.85% have lifespans less than 10.4 + 3 * 1.91 = 16.13 years.

Therefore, we can estimate that the probability of a meerkat living less than 16.1 years is about 49.85%.