Question

Consider a bell-shaped symmetric distribution with mean of 16 and standard deviation of 1.5. Approximately what percentage of data lie between 13 and 19?

Answer 1

Answer: 95.45 %

Explanation:

Given : The distribution is bell shaped , then the distribution must be normal distribution.

Mean :
`\mu=\ 16`

Standard deviation :
`\sigma= 1.5`

The formula to calculate the z-score :-

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

For x = 13

`z=(13-16)/(1.5)=-2`

For x = 19

`z=(19-16)/(1.5)=2`

The p-value =
`P(-2<z<2)=P(z<2)-P(z<-2)`

`0.9772498-0.0227501=0.9544997\approx0.9545`

In percent,
`0.9545*100=95.45\%`

Hence, the percentage of data lie between 13 and 19 = 95.45 %