Question

The lifespans of lions in a particular zoo are normally distributed. The average lion lives 12.5 years; the standard

deviation is 2.4 years,
Use the empirical rule (68 - 95 - 99.7%) to estimate the probability of a lion living longer than 10.1 years.

Answer 1

16

Explanation:

Answer 2

We have been given that the lifespans of lions in a particular zoo are normally distributed. The average lion lives 12.5 years; the standard deviation is 2.4 years. We are asked to find the probability of a lion living longer than 10.1 years using empirical rule.

First of all, we will find the z-score corresponding to sample score 10.1.

`z=(x-\mu)/(\sigma)`, where,

z = z-score,

x = Random sample score,

`\mu` = Mean

`\sigma` = Standard deviation.

`z=(10.1-12.5)/(2.4)`

`z=(-2.4)/(2.4)`

`z=-1`

Since z-score of 10.1 is
`-1`. Now we need to find area under curve that is below one standard deviation from mean.

We know that approximately 68% of data points lie between one standard deviation from mean.

We also know that 50% of data points are above mean and 50% of data points are below mean.

To find the probability of a data point with z-score
`-1`, we will subtract half of 68% from 50%.

`(68\%)/(2)=34\%`

`50\%-34\%=16\%`

Therefore, the probability of a lion living longer than 10.1 years is approximately 16%.