Question

Consider the following information: Driver's license test scores for 2,000 high school students were normally distributedwith a mean of 80 and a standard distribution of 4.About how many students scored higher than 88?The answers are 50 32010001680

Answer 1

According to the information given in the exercise:

- The number of students is 2,000.

- The driver's licenses test scores were normally distributed.

- The Mean is:

$\mu=80$

- And:

$\sigma=4$

You need to know the number of students that scored higher than 88. Therefore:

$x=88$

Now you can find the probability of "x" is greater than 88. This is:

$P(x>88)$

In order to calculate it, you need to approximate to a Normal Standard Distribution:

1. Remember that Z-statistic:

$Z=\frac{x-\mu}{\sigma}=\frac{88-80}{4}=2$

Then:

$P(x>88)=P(Z>2)$

2. Now you need to use the Normal Standard Table to find:

$P(Z>2)$

This is:

$P(Z>2)=0.0228$

3. Therefore, you can determine that the expected number of students that scored higher than 88 is:

$0.0228\cdot2000\approx50$

Hence, the answer is: First option.