High School

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 your answer to two decimal places.)

A. 9.47 hours
B. 5.53 hours
C. 0.10 hours
D. 10.37 hours

Answer :

Final answer:

Mackenzie studies approximately 9.47 hours per week which corresponds to her score at the 46th percentile in her statistics course.

Explanation:

This question involves the use of statistics to relate Mackenzie's study time to her score percentile in order to solve for the unknown study hours. We extract relevant information from the problem: average study hours (mean) is 9.92, standard deviation is 4.54, and Mackenzie's score percentile is 46th, which is converted to a standard Z-score (for the 46th percentile) of -0.1.

In a normal distribution, the formula connecting Z-score, standard deviation, mean and the actual observed value (X) is: Z = (X - Mean) / Standard Deviation

We thus re-arrange this equation to solve for X(which represents Mackenzie's study hours): X = (Z * Standard Deviation) + Mean

When we plug known values, we obtain: X = (-0.1 * 4.54) + 9.92, which evaluates to approximately 9.47 hours, corresponding to option a.

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