Question

A)Adult men have heights with a mean of 69.0 inches and a standard deviation of 2.8 inches. Find the height of a man with a z-score of 0.8214 (to 4 decimal places)

B)For a 4-unit class like Statistics, students should spend average of 12 hours studying for the class. A survey was done on 29 students, and the distribution of total study hours per week is bell-shaped with a mean of 13 hours and a standard deviation of 3.2 hours.

Use the Empirical Rule to answer the following questions.

1.68% of the students spend between ____ hours and____ hours on Statistics each week.
2.95% of the students spend between _____ hours and ___ hours on Statistics each week.
3.99.7% of the students spend between ____ hours and____ hours on Statistics each week.

C)The five number summary of a dataset was found to be:

45, 47, 60, 64, 67

An observation is considered an outlier if it is below:

An observation is considered an outlier if it is above:

Answer 1

Solution:-

A) The height of a man with a z-score of 0.8214 is 71.299.

Mean = 69.0, S.D = 2.80

By applying normal distribution:-

x = 71.299

B)

Mean = 13, S.D = 3.2, n = 29

The values of x for z = + 1, + 2, + 3

By applying normal distribution:-

x_68% = 12.406, 13.594

x_95% = 11.811, 14.188

x_99.7% = 11.217, 14.783

1) 68% of the students spend between 12.406 hours and 13.594 hours on Statistics each week.
2) 95% of the students spend between 11.811 hours and 14.188 hours on Statistics each week.
3) 99.7% of the students spend between 11.217 hours and 14.783 hours on Statistics each week.