Question

The ages of students in a school are normally distributed with a mean of 15 years and a standard deviation of 2 years. Approximately what percent of the students are between 14 and 18 years old?

Answer 1

62.47%

Explanation:

Answer 2

We have been given that the ages of students in a school are normally distributed with a mean of 15 years and a standard deviation of 2 years.

We are asked to find the percentage of students that are between 14 and 18 years old.

First of all, we will find z-score corresponding to 14 and 18 using z-score formula.

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

`z=(14-15)/(2)`

`z=(-1)/(2)`

`z=-0.5`

Similarly, we will find the z-score corresponding to 18.

`z=(18-15)/(2)`

`z=(3)/(2)`

`z=1.5`

Now we will find the probability of getting a z-score between
`-0.5` and
`1.5` that is
`P(-0.5<z<1.5)`.

`P(-0.5<z<1.5)=P(z<1.5)-P(z<-0.5)`

Using normal distribution table, we will get:

`P(-0.5<z<1.5)=0.93319-0.30854`

`P(-0.5<z<1.5)=0.62465`

Let us convert
`0.62465` into percentage.

`0.62465* 100\%=62.465\%\approx 62.5\%`

Therefore, approximately
`62.5\%` of the students are between 14 and 18 years old.