Question

the lifespans of tigers in a particular zoo are normally distributed. the average tiger lives 22.4 years; the standard deviation is 2.7 years. use the empirical rule (68 - 95 - 99.7%) to estimate the probability of a tiger living longer than 14.3 years. %

Explanation:

Step1: Calculate z-score for 14.3

$z = \frac{14.3 - 22.4}{2.7} = -3$

Step2: Apply empirical rule

99.7% of data within $\mu \pm 3\sigma$. Data below $\mu - 3\sigma$ is $\frac{100\% - 99.7\%}{2} = 0.15\%$.

Step3: Find probability above 14.3

$100\% - 0.15\% = 99.85\%$

Answer:

99.85%