Question

Consider the following information: Driver's license test scores for 2,000 high school students were normally distributed with a mean of 80 and a standard distribution of 4. What percentage of students scored between 76 and 88?1- 34% 2- 68%3- 81.50%4- 79.5%

Answer 1

Given:

Driver's license test scores for 2,000 high school students were normally distributed

The mean = μ = 80

And, the standard distribution = σ = 4

We will find the percentage of students who scored between 76 and 88

We will use the z-score to find the answer

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

So, the values of (z) when x = {76, 88} will be as follows:

$\begin{gathered} x=76\rightarrow z=\frac{76-80}{4}=-\frac{4}{4}=-1 \\ x=88\rightarrow z=\frac{88-80}{4}=\frac{8}{4}=2 \end{gathered}$

We will use the following chart to find the probability between -1 and 2

So, as shown, the probability will be:

$34\%+34\%+13.5\%=81.5\%$

So, the answer will be option 3) 81.5%