In one statistics course, students reported studying an average of 9.92 hours a week, with a standard deviation of 4.54.The professor tells Mackenzie she scored at the 46th percentile.How many hours does she study per week? (Round z score to two decimal places.)
A) 0.10 hours
B) 5.53 hours
C) 9.47 hours
D) 10.37 hours

Question

Quizplus · Accepted Answer

To find the number of hours Mackenzie studies per week, given she is at the 46th percentile, we first need to find the z-score corresponding to the 46th percentile. The z-score for the 46th percentile is approximately -0.10 (since the 50th percentile, which has a z-score of 0, is the mean, and the 46th percentile is slightly below the mean). Using the z-score formula: $z = \frac{(X - \mu)}{\sigma}$, where $X$ is the value we're looking for, $\mu$ is the mean, and $\sigma$ is the standard deviation, we can rearrange the formula to solve for $X$: $X = z\sigma + \mu$. Substituting the given values: $X = -0.10(4.54) + 9.92$, we get $X \approx 9.47$ hours.

In One Statistics Course, Students Reported Studying an Average of 9.92