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 less than 14.3 years.

Explanation:

Step1: Calculate number of standard - deviations

Find how many standard deviations 14.3 is from the mean. Let $\mu = 22.4$ (mean) and $\sigma=2.7$ (standard deviation). Calculate $z=\frac{14.3 - 22.4}{2.7}=\frac{- 8.1}{2.7}=-3$.

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., $P(\mu - 3\sigma

Answer:

0.15%