Question

the lifespans of meerkats in a particular zoo are normally distributed. the average meerkat lives 13.1 years; the standard deviation is 1.5 years. use the empirical rule (68 - 95 - 99.7%) to estimate the probability of a meerkat living between 16.1 and 17.6 years.

Explanation:

Step1: Identify mean and standard deviation

Mean $\mu = 13.1$, standard deviation $\sigma = 1.5$

Step2: Calculate z-scores for 16.1 and 17.6

For 16.1: $z = \frac{16.1 - 13.1}{1.5} = 2$
For 17.6: $z = \frac{17.6 - 13.1}{1.5} = 3$

Step3: Apply empirical rule

99.7% within $\mu \pm 3\sigma$, 95% within $\mu \pm 2\sigma$. The area between $z=2$ and $z=3$ is $\frac{99.7\% - 95\%}{2} = 2.35\%$

Answer:

2.35%