For a 4-unit class like Statistics, students should spend average of 12 hours studying for the class. A survey was done on 22 students, and the distribution of total study hours per week is bell-shaped with a mean of 12 hours and a standard deviation of 3.4 hours. Use the Empirical Rule to answer the following questions. a) 68% of the students spend between hours andb) 95% of the students spend between hours andc) 99.7% of the students spend between hours and hours on Statistics each week. hours on Statistics each week. hours on Statistics each week.

Answer: a) About 68% of the students spend between 8.6 hours and 15.4 hours.

b) About 95% of the students spend between 5.2 hours and 18.8 hours.

c) About 99.7% of the students spend between 1.8 hours and 22.2 hours.

Step-by-step explanation:

The famous Empirical rule states that;

About 68% of the population lies with one standard deviation from the mean. About 95% of the population lies with two standard deviations from the mean. About 99.7% of the population lies with three standard deviations from the mean.

Since, the distribution of total study hours per week is bell-shaped that means it follows normal distribution.

Mean = 12 hours

Standard deviation: 3.4 hours

Now,

a) Mean± Standard deviation = 12 ± 3.4 hours

= (12-3.4, 12+3.4) hours

= (8.6, 15.4) hours

∴About 68% of the students spend between 8.6 hours and 15.4 hours.

b) Mean± 2 Standard deviation = 12 ± 2 (3.4) hours

= 12 ± 6.8 hours

= (12-6.8, 12+6.8) hours

= (5.2,18.8) hours

∴About 95% of the students spend between 5.2 hours and 18.8 hours.

c) Mean± 3 Standard deviation = 12 ± 3 (3.4) hours

= 12 ± 10.2 hours

= (12-10.2, 12+10.2) hours

= (1.8,22.2) hours

∴About 99.7% of the students spend between 1.8 hours and 22.2 hours.