Question

The grades on a physics midterm at Covington have an average of μ=72 and σ=2.0 If Stephanie scored 1.23 standard deviations above the mean.
a. What score did Stephanie get on the exam?
b. What percent of students scored better than Stephanie?

Answer 1

Answer:

a) She scored 74.46 on the exam.

b) 11% of the students scored better than Stephanie.

Step-by-step explanation:

The z-score measures how many standard deviation a score X is above or below the mean. It is given by the following formula:

$Z = \frac{X - \mu}{\sigma}$

In which $\mu$ is the mean and $\sigma$ is the standard deviation.

In this problem, we have that:

$\mu = 72, \sigma = 2$

a. What score did Stephanie get on the exam?

Stephanie scored 1.23 standard deviations above the mean. This means that her z-score is $Z = 1.23$

We want to find X

$Z = \frac{X - \mu}{\sigma}$

$1.23 = \frac{X - 72}{2}$

$X - 72 = 2*1.23$

$X = 74.46$

She scored 74.46 on the exam.

b. What percent of students scored better than Stephanie?

Each z-score has a pvalue, which is the percentile of the score. We look this pvalue at the z table.

$Z = 1.23$ has a pvalue of 0.89.

This means that Stephanie's score is in the 89th percentile, which means that she scored more than 89% of the students and scored less than 100-89 = 11% of the students.

So 11% of the students scored better than Stephanie.