Instructions: Please print out and complete the following assignment writing your answers clearly and showing your work directly on the  assignment. Please circle your answers (unless it is in a chart/graph already), and staple the pages together when you are finished. Be sure to turn the assignment in at the beginning of class on Tuesday, September 22. Late homeworks cannot be accepted.

1. The following table is given:

R=300 R=400 R=500 P(B=b)

B=20 .2

B=25 .2 .6

P(R=r) .3 .25 1

a. Fill in the missing values of the table.

b. Calculate E[R | B=20]

c. Calculate E[R | B=25]

2. Dress for Success Business Clothing, a formal-wear company, has outlets in several cities in the region.The sales department aired a commercial for a men's business suit on selected local TV stations prior to a sale starting on Saturday and ending Sunday. The sales  department obtained the information forSaturday-Sunday men's suit sales at the various outlets and paired it with the number of times the advertisement was shown on the local TV stations. The goal is to find whether there is any relationship  between the number of times the advertisement was aired and men's suit sales. Here is the data:

a. Draw and label a scatter diagram using the given data:

b. Determine the correlation coefficient. (If you use Excel, please attach a printout of yourspreadsheet and highlight the numbers that you   plug into the formulas).

c. Interpret the correlation coefficient (both strength and direction). What does this suggest to the sales department?

3. The town council of Smithburg is considering increasing the number of police to try to reduce crime.

While making this decision, the council decided to research the relationship between the number of police and the number of crimes reported. They gathered the following information from 8 other cities:

City Police Number of

Crimes

City Police Number of

Crimes

a. Determine the regression equation with crimes as the dependent variable and police as the independent variable. Calculate using the approach shown in class-either by hand or with Excel. (If you use Excel, please attach a printout of your spreadsheet and highlight the numbers that you plug into the formulas).

b. Estimate the number of crimes for a city with 20 police officers.