the lifespans of meerkats in a particular zoo are normally distributed. the average meerkat lives 13.1…

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 less than 14.6 years.

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 less than 14.6 years.

Answer

Explanation:

Step1: Calculate the z - score

The z - score formula is $z=\frac{x-\mu}{\sigma}$, where $x = 14.6$, $\mu=13.1$ and $\sigma = 1.5$. So $z=\frac{14.6 - 13.1}{1.5}=\frac{1.5}{1.5}=1$.

Step2: Apply the empirical rule

The empirical rule for a normal distribution states that about 68% of the data lies within 1 standard - deviation of the mean ($\mu\pm\sigma$), which means 34% of the data lies between $\mu$ and $\mu+\sigma$. The data to the left of the mean ($\mu$) is 50%. Since $z = 1$, the probability of a value being less than $\mu+\sigma$ is $50%+34% = 84%$.

Answer:

84%