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.
