Question

For a 4-unit class like Statistics, students should spend average of 12 hours studying for the class. A survey was done on 24 students, and the distribution of total study hours per week is bell-shaped with a mean of 13 hours and a standard deviation of 2.8 hours. Use the Empirical Rule to answer the following questions.
a) 68% of the students spend between hours and hours on Statistics each week.
b) 95% of the students spend between hours and hours on Statistics each week.
c) 99.7% of the students spend between hours and hours on Statistics each week.

Answer 1

Answer:

a) 68% of the students spend between 10.2 hours and 15.8 hours on Statistics each week.

b) 95% of the students spend between 7.4 hours and 18.6 hours on Statistics each week.

c) 99.7% of the students spend between 4.6 hours and 21.4 hours on Statistics each week.

Step-by-step explanation:

The Empirical Rule states that, for a normally distributed(bell-shaped) random variable:

68% of the measures are within 1 standard deviation of the mean.

95% of the measures are within 2 standard deviation of the mean.

99.7% of the measures are within 3 standard deviations of the mean.

In this problem, we have that:

Mean = 13 hours

Standard deviation = 2.8 hours.

a) 68% of the students spend between hours and hours on Statistics each week.

Within 1 standard deviation of the mean.

13 - 2.8 = 10.2 hours

13 + 2.8 = 15.8 hours

68% of the students spend between 10.2 hours and 15.8 hours on Statistics each week.

b) 95% of the students spend between hours and hours on Statistics each week.

Within 2 standard deviations of the mean

13 - 2*2.8 = 7.4 hours

13 + 2*2.8 = 18.6 hours

95% of the students spend between 7.4 hours and 18.6 hours on Statistics each week.

c) 99.7% of the students spend between hours and hours on Statistics each week.

Within 3 standard deviations of the mean

13 - 3*2.8 = 4.6 hours

13 + 3*2.8 = 21.4 hours

99.7% of the students spend between 4.6 hours and 21.4 hours on Statistics each week.