the lifespans of tigers in a particular zoo are normally distributed. the average tiger lives 22.4 years…

Explanation:

Step1: Calculate z - score

The z - score formula is $z=\frac{x-\mu}{\sigma}$, where $x = 14.3$, $\mu=22.4$, and $\sigma = 2.7$. So $z=\frac{14.3 - 22.4}{2.7}=\frac{-8.1}{2.7}=- 3$.

Step2: Apply empirical rule

The empirical rule for a normal distribution states that about 99.7% of the data lies within 3 standard - deviations of the mean, i.e., between $z=-3$ and $z = 3$. The total area under the normal curve is 100%. The area to the left of $z=-3$ is $\frac{100 - 99.7}{2}=0.15%$.

Step3: Find the probability of living longer than 14.3 years

The probability of a tiger living longer than 14.3 years (corresponding to $z=-3$) is $100 - 0.15=99.85%$.

Answer:

99.85