Statistics Assignment

Chapter 4

Descriptive Statistics

Chapter 5

Probability

Chapter 6

Discrete Probability Distributions

Upload the completed assignment using the file extension format Lastname_Firstname_Week2.doc.

Assignment

(32 points due by 11 pm July 7th)

Note: You can team up with one of your classmates to complete the assignment (not more than two in a team); if you want to work on the assignment individually, that’s also fine. If you are working in teams, then only one submission is required per team; include both the team members’ last names as part of the assignment submission file name as well as in the assignment submission document.

Please provide detailed solutions to the following problems/exercises (4 problems/exercises x 8 points each):

1) The file ‘Energy’ contains the per capita energy consumption (in kilowatt-hours), for each of the 50 states and the District of Columbia during a recent year.

a) Compute the mean, variance, and standard deviation for the population.

b) What proportion of these states has per capita energy consumption within + or – 1 standard deviation of the mean, within + or – 2 standard deviations of the mean, and within + or – 3 standard deviations of the mean?

c) Compare your findings with what would be expected based on the empirical rule.

d) Repeat a) through c) with the District of Columbia removed. Have the results changed?

2) Higher productivity in the economy usually translates into higher increases in hourly compensation to workers. However, management often delays increasing compensation to show profits for the company. In the data file ‘Productivity’, for the period 1990 to 2001, productivity is labeled as high for each quarter if the annualized economic growth is at least 2%. In addition, the amount pay increase during the quarter is labeled as large if the hourly compensation is at least 4% on an annualized basis.

a) Suppose that a quarter is randomly selected, what is the probability that this quarter has high productivity growth and has a large pay increase?

b) If a quarter has high productivity, what is the probability that the quarter has a small pay increase?

c) Are the events of productivity and amount of hourly pay increase independent? Explain.

3) Materials for a food processing plant are supplied by four companies. The following table lists the percentage of defective items from each company and the percentage of materials supplied by that company to the food processing plant.

	Percentage of Materials Supplied	Percentage of Defective Materials Supplied
Supplier 1	40	2
Supplier 2	5	10
Supplier 3	20	8
Supplier 4	35	3

a) Determine the percentage of all materials that are defective.

b) Given that a material supplied to the plant is defective, what is the probability that it came from supplier 3?

4) Find the probabilities of the following events for a binomial random variable with n = 10, and p = .5.

a) Exactly two successes

b) More than two successes

c) No more than 2 successes

d) Less than 2 successes

e) At least 2 successes