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 14 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 = = 14 hours.

standard deviation = = 3.4 hours.

n = 24

= = 14 hours.

= / n = 3.4 / 24 = 0.69 hours.

Using Empirical rule,

a) P( - < <   + ) = 68%

= P( 14 - 0.69 <   < 14 + 0.69 ) = 68%

= P( 13.31 <   < 14.69 ) =68%

68% of the students spend between 13.31 hours and 14.69 hours on Statistics each week.

b) P( - 2 < <   + 2 ) = 95%

= P( 14 - 2 * 0.69 < < 14 + 2 * 0.69 ) = 95%

= P( 14 - 1.38 < < 14 + 1.38 ) = 95%

=P( 12.62 < < 15.38 ) = 95%

95% of the students spend between 12.62 hours and 15.38 hours on Statistics each week.

c) P( - 3 < <   + 3 ) = 99.7%

= P( 14 - 3 * 0.69 < < 14 + 3 * 0.69) = 99.7%

= P( 14 - 2.07 < < 14 + 2.07) = 99.7%

=P( 11.93 < < 16.07 ) = 99.7%

99.7% of the students spend between 11.93 hours and 16.07 hours on Statistics each week.