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

Step-by-step explanation:

The question is incomplete. The complete question is:

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. Use the empirical rule (68-95-99.7%)

to estimate the probability of a meerkat living longer than 16.1

Solution:

Let x be a random variable representing the lifespans of meerkats in a particular zoo. With the mean and standard deviation given, then the Empirical Rule says the that

1) About 68% of the x values lie between 1 standard deviation below and above the mean.

2) About 95% of the x values lie between 2 standard deviations below and above the mean.

3) About 99.7% of the x values lie between 3 standard deviations below and above the mean.

From the information given,

mean = 10.4 years

Standard deviation = 1.9 years

x = 16.1 years

Therefore,

3 standard deviations = 3 * 1.9 = 5.7 years

16.1 = 10.4 ± 5.7

Therefore, x is 3 standard deviations from the mean. Therefore, the probability of a meerkat living longer than 16.1 is 99.7%