Question

the lifespans of gorillas in a particular zoo are normally distributed. the average gorilla lives 20.8 years; the standard deviation is 3.1 years. use the empirical rule (68 - 95 - 99.7%) to estimate the probability of a gorilla living less than 23.9 years. %

Explanation:

Step1: Identify mean and standard deviation

Mean $\mu = 20.8$, standard deviation $\sigma = 3.1$

Step2: Calculate z-score for 23.9

$z = \frac{23.9 - 20.8}{3.1} = 1$

Step3: Apply empirical rule

68% within $\mu \pm \sigma$, so 34% above mean to $\mu+\sigma$. Probability below $\mu+\sigma$ is 50% + 34% = 84%

Answer:

84%