Question

For a 4-unit class like Statistics, students should spend average of 12 hours studying for the class. A survey was done on 23 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. Question Help: C Written Example Message instructor

Answer 1

Obtain the 68% of the students spends between the number ofhours on Statistics each week. The 68% of the students spends betweenthe number of hours on Statistics each week are obtainedbelow: The Empirical rule for any normal distribution is given below: • 68% of the observations fall in the interval [7 -5.7+s] • 95% of the observations fallin the interval [7 -25.7+2s] • 99.7% of the observations fall in the interval [7 – 35,7 +35] By, the empirical rule, it is clear that Let X denotes the average study hours per week which follows nomal distribution with mean 13 hours and standard deviation of 3.4 hours. That is 1 =13,5 =3.4. One standard deviation above and below the meanis, [1-5,+s] [13-3.4,13+3.4] = [9.6.16.4] The 68% of the students spends betweenthe 9.6 hours and 16.4 hours on Statistics each week.

Obtain the 95% of the students spends between the number of hours on Statistics each week. The 95% of the students spends betweenthe number of hours on Statistics each week are obtainedbelow: Two standard deviation above and below the meanis, [7–25.7+25]=[13-2 (3.4),13+2 (3.4)] = [13-6.8.13+6.8] =[6.2,19.8] The 95% of the students spends betweenthe 6.2 hours and 19.8 hours on Statistics each week.

Obtain the 99.7% of the students spends between the number of hours on Statistics eachweek. The 99.7% of the students spends between the number of hours on Statistics eachweek are obtained below: Two standard deviation above and below the meanis, [7–35,2+35] = [13–3(3.4),13+3(3.4)] = [13–10.2.13+10.2] = [2.8.23.2] The 99.7% of the students spends between the 2.8 hours and 23.2 hours on Statistics each week.

Obtain the height of a man with a standard nomal score of-1.1429. The height of a man with a standardnomal score of-1.1429 is obtainedbelow: Let X denotes the men heights which follows nomal distribution with mean of 69.0 inches and the standard deviation of 2.8 inches. That is, 4 = 69.0.5 = 2.8. X- Z=- X-69.0 -1.1429= 2.8 -1.1429x2.8 = X-69.0 -3.20012 = X-69.0 X = 69.0-3.20012 = 65.79988 65.7999 The height of a man with a standard nomal score of-1.1429 is 65.7999.