A study reported by the Michigan State campus newspaper stated that the average time MSU students spent studying last month was is 58.3 hours, with a standard deviation of 14 hours.If the study time distribution is normal, what percentage of students spent more than 70 hours studying?
A).3749
B).2454
C).2005
D).1772
E).2823

Question

Quizplus · Accepted Answer

To find the percentage of students who spent more than 70 hours studying, we use the Z-score formula: Z = (X - μ) / σ, where X is the value of interest (70 hours), μ is the mean (58.3 hours), and σ is the standard deviation (14 hours). Plugging in the values, we get Z = (70 - 58.3) / 14 = 11.7 / 14 = 0.8357. Looking up 0.8357 in the Z-table gives us the area to the left of Z, which is approximately 0.7977. To find the percentage of students who spent more than 70 hours studying, we subtract this from 1 (since we want the area to the right of Z) and get 1 - 0.7977 = 0.2023, or 20.23%. This corresponds to choice C, 20.05%, which is the closest to our calculated value.

A Study Reported by the Michigan State Campus Newspaper Stated