Solve the problem.
-Scores on a test are normally distributed with a mean of 72 and a standard deviation of 5. What is the percentile for an exam score of 84? Round the percentile to the nearest tenth.
A)99.2
B)99.4
C)2.4
D)2

Question

Quizplus · Accepted Answer

To find the percentile for an exam score of 84, we first calculate the z-score using the formula $z = \frac{X - \mu}{\sigma}$, where $X$ is the score, $\mu$ is the mean, and $\sigma$ is the standard deviation. Substituting the given values, we get $z = \frac{84 - 72}{5} = \frac{12}{5} = 2.4$. Looking up 2.4 in a standard normal distribution table or using a calculator, we find that the area to the left (which represents the percentile) is approximately 0.9918 or 99.2%. This means that an exam score of 84 is at the 99.2nd percentile.

Solve the Problem. -Scores on a Test Are Normally Distributed with a Mean