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.
, where,
z = z-score,
x = Random sample score,
= Mean
= Standard deviation.
![z=\frac{10.1-12.5}{2.4}](https://tex.z-dn.net/?f=z%3D%5Cfrac%7B10.1-12.5%7D%7B2.4%7D)
![z=\frac{-2.4}{2.4}](https://tex.z-dn.net/?f=z%3D%5Cfrac%7B-2.4%7D%7B2.4%7D)
![z=-1](https://tex.z-dn.net/?f=z%3D-1)
Since z-score of 10.1 is
. 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
, we will subtract half of 68% from 50%.
![\frac{68\%}{2}=34\%](https://tex.z-dn.net/?f=%5Cfrac%7B68%5C%25%7D%7B2%7D%3D34%5C%25)
![50\%-34\%=16\%](https://tex.z-dn.net/?f=50%5C%25-34%5C%25%3D16%5C%25)
Therefore, the probability of a lion living longer than 10.1 years is approximately 16%.
Answer:
Mean: 44
Step-by-step explanation:
1. 24 + 36 + 52 + 48 + 64 + 40 = 264
2. 264 divided by 6 = 44
(I divided it by 6 because there are 6 numbers (data points).)
She needs to wash 7 cars.
Answer:-8,-2,4,10
Step-by-step explanation:
3/5 of 42000 is 25200 so the amount of people who did not vote is 16800 because the beginning amount of 42000 subtracted from 25200 gives you the final answer
If that's confusing the answer is 16800 votes didn't pick the winner