Question

5) [5 pts.] A student scores 91 on the midterm exam for Psych 60. Assume the class scores are normally distributed, with a mean (µ) of 65 and standard deviation (σ) of 15. The student’s exam score corresponds to what percentile?

Answer 1

Answer:

The score corresponds to the 95.82th percentile.

Explanation:

To formula to calculate the percentile in a  normal distribution is:

$X=\mu+Z\sigma$

Where $X$ is the value of the variable, $\mu$ is the mean, $Z$ is the value from the standard normal distribution for the percentile. In this case, you have $X$ and want to know the value of $Z$.

$X=\mu+Z\sigma\\Z\sigma=X-\mu\\Z=\frac{X-\mu}{\sigma} \\Z=\frac{91-65}{15}\\Z=\frac{26}{15}\\Z=1.73$

The value of $Z=1.73$ in the table of the standard normal distributions gives a value of 0.9582, which means the score is in the 95.82th percentile.