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:

Given,

mean = 12

standard deviation = 2.8

n = 24

a)

By using Empirical rule, 68% of the Students spend between

consider,

xbar +/- z*sigma/sqrt(n)

substitute values

= 12 +/- 1*2.8/sqrt(24)

= 12 - 0.572 , 12 + 0.572

= (11.428 , 12.572)

So 68% of the Students spend between 11.428 hours and 12.572 hours on Statistics each week.

b) Now 95% of the students spends

xbar +/- z*sigma/sqrt(n)

substitute values

12 +/- 2*2.8/sqrt(24)

= 12 +/- 1.143

= 12 - 1.143 , 12 + 1.143

= (10.857 , 13.143)

So 95% of the Students spend between 10.857 hours and 13.143 hours on Statistics each week.

c) 99.7% of the Students spend

xbar +/- z*sigma/sqrt(n)

substitute values

12 +/- 3*2.8/sqrt(24)

= 12 +/- 1.715

= 12 - 1.715 , 12 + 1.715

= (10.285 , 13.715)

99.7% of the Students spend between 10.285 hours and 13.715 hours