the lifespans of gorillas in a particular zoo are normally distributed. the average gorilla lives 16 years…

Explanation:

Step1: Calculate the number of standard - deviations for lower bound

The lower bound is $14.3$ years. The mean $\mu = 16$ years and the standard deviation $\sigma=1.7$ years. The number of standard - deviations $z_1$ for the lower bound is $z_1=\frac{14.3 - 16}{1.7}=\frac{- 1.7}{1.7}=-1$.

Step2: Calculate the number of standard - deviations for upper bound

The upper bound is $19.4$ years. The number of standard - deviations $z_2$ for the upper bound is $z_2=\frac{19.4 - 16}{1.7}=\frac{3.4}{1.7}=2$.

Step3: Apply the empirical rule

The empirical rule states that about $68%$ of the data lies within $1$ standard - deviation of the mean ($\mu\pm\sigma$), about $95%$ of the data lies within $2$ standard - deviations of the mean ($\mu\pm2\sigma$), and about $99.7%$ of the data lies within $3$ standard - deviations of the mean ($\mu\pm3\sigma$). The area between $z=-1$ and $z = 2$ can be found by considering the areas within the standard - deviation intervals. The area within $z=-1$ and $z = 1$ is $68%$, and the area within $z=-2$ and $z = 2$ is $95%$. The area between $z = 1$ and $z = 2$ is $\frac{95 - 68}{2}=13.5%$. The area between $z=-1$ and $z = 2$ is $68%+13.5% = 81.5%$.

Answer:

$81.5$