Question

For a 4-unit class like Statistics, students should spend an average of 12 hours studying for the class. A survey was done on 21 students, and the distribution of total study hours per week is bell-shaped with a mean of 13 hours and a standard deviation of 3 hours. Use the Empirical Rule to answer the following questions. a) 68% of the students spend between which hours on Statistics each week?

A) 7 hours and 19 hours
B) 10 hours and 16 hours
C) 8 hours and 14 hours
D) 9 hours and 15 hours

Answer 1

Using the Empirical Rule, 68% of the students spend between 10 and 16 hours studying Statistics each week.

Step-by-step explanation:

The Empirical Rule states that for a bell-shaped distribution, approximately 68% of the data will fall within one standard deviation of the mean, 95% within two standard deviations, and 99.7% within three standard deviations. Considering the survey of 21 students about their study hours, we have a mean of 13 hours and a standard deviation of 3 hours.

To find the range of hours where 68% of the students spend studying each week:

• Add and subtract one standard deviation from the mean: 13 hours ± 3 hours.
• This gives us a range of 10 hours to 16 hours.

Hence, the correct answer is B) 10 hours and 16 hours.