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

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.

$z=\frac{x-\mu}{\sigma}$

$z=\frac{14-15}{2}$

$z=\frac{-1}{2}$

$z=-0.5$

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

$z=\frac{18-15}{2}$

$z=\frac{3}{2}$

$z=1.5$

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.

$0.62465\times 100\%=62.465\%\approx 62.5\%$

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

Answer 2

Answer:

62.47%

Step-by-step explanation: