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 for
Saturday-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:
Location of TV
Station
Number of
Airings
SaturdaySunday
Sales
($ thousands)
Pleasant Valley 4 15
Feagaville 2 8
Leesburg 5 21
Oxford 26 24
Woodsboro 3 17
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 your
spreadsheet 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
Pleasant Valley 15 17 Holgate 17 7
Feagaville 17 13 Woodsboro 12 21
Leesburg 25 5 Danville 11 19
Oxford 27 7 Athens 22 6
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.
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