Question

For a 4-unit class like Statistics, students should spend average of 12 hours studying for the class. A survey was done on 20 students, and the distribution of total study hours per week is bell-shaped with a mean of 13 hours and a standard deviation of 3.4 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

Solution :

Given that,

mean = = 13 hours.

standard deviation = = 3.4 hours.

n = 20

= = 13 hours.

= / n = 3.4 / 20 = 0.76 hours.

a) P( - < <   + ) = 68%

= P( 13 - 0.76 <   < 13 + 0.76 ) = 68%

= P( 12.24 <   < 13.76 ) =68%

68% of the students spend between 12.24 hours and 13.76 hours on Statistics each week

b) P( - 2 < <   + 2 ) = 95%

= P( 13 - 2 * 0.76 < < 13 + 2 * 0.76 ) = 95%

= P( 13 - 1.52 < < 13 + 1.52 ) = 95%

=P( 11.48 < < 14.52 ) = 95%

95% of the students spend between 11.48 hours and 14.52 hours on Statistics each week

c) P( - 3 < <   + 3 ) = 99.7%

= P( 13 - 3 * 0.76 < < 13 + 3 * 0.76) = 99.7%

= P( 13 - 2.28 < < 13 + 2.28 ) = 99.7%

=P( 10.72 < < 15.28 ) = 99.7%

99.7% of the students spend between 10.72 hours and 15.28 hours on Statistics each week