Question

STS Solve Applications Involving Normal DistributionsA set of 1200 exam scores is normally distributed with a mean of 84 and standard deviation of 9. Use theEmpirical Rule to complete the statements below.

Answer 1

Let us upload the bell curve for standard normal distribution

Given that

`\begin{gathered} \mu=84 \\ \sigma=9 \\ \end{gathered}`

15) How many students scored higher than 84

Therefore, the number of students that will score higher than 84 which is the mean will be 50% from the bell curve standard normal distribution.

Hence, the answer is 50%.

19) How many students scored lower than 75?

To get the number of students that score lower than 75, we will subtract 1standard deviation from the mean.

`\begin{gathered} \mu-\sigma=84-9=75 \\ \end{gathered}`

Hence, the number of students will be

`9.2\text{ \%+4.4\%+1.7\%+0.5\%+0.1\%=15.9\%}`

The answer is 15.9%.

20) How many students scored lower than 93?

To get the number of students that score lower than 93, we will add 1standard deviation from the mean.

`\mu+\sigma=84+9=93`

Hence, the number of students will be

`100\text{ \% -(9.2+4.4+1.7+0.5+0.1)\%=100\%-15.9\%=84.1\%}`

The answer is 84.1%.