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

The score corresponds to the 95.82th percentile.

Step-by-step 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=(X-\mu)/(\sigma) \\Z=(91-65)/(15)\\Z=(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.