Motivation Level 
Talent 

High 
Medium 
Low 
Total 

High 
6 
18 
6 

Medium 
21 
35 
6 

Low 
12 
6 
2 

Total 
Q1. Are high motivation and high talent independent? Justify your answer.
Adrian sells cars for Honest Joe’s car dealership. Adrian has never sold more than three cars in a given week. Given X is the number of cars sold by Adrian in a week, the probability distribution of X is summarized in the following table:
X 
0 
1 
2 
3 
P(X) 
p 
0.45 
0.25 
0.05 
(a) What is the probability of Adrian selling zero cars?
(b) What is the probability of Adrian selling at least two cars?
(c) What is the probability of Adrian selling no more than one car?
(d) Draw the probability distribution in a graphical form.
(e) Adrian gets paid a bonus of $500 if he sells one car per week. For each additional car sold per week Adrian receives $300. Calculate his mean bonus.
( 1 )
The following cross tablulation have been provided. The row and column total have been calculated and they are shown below:
Observed  Column 1  Column 2  Column 3  Total 
Row 1  6  18  6  30 
Row 2  21  35  6  62 
Row 3  12  6  2  20 
Total  39  59  14  112 
Expected Values  Column 1  Column 2  Column 3  Total 
Row 1  39*30/112 = 10.446  59*30/112 = 15.804  14*30/112 = 3.75  30 
Row 2  39*62/112 = 21.589  59*62/112 = 32.661  14*62/112 = 7.75  62 
Row 3  39*20/112 = 6.964  59*20/112 = 10.536  14*20/112 = 2.5  20 
Total  39  59  14  112 
Null and Alternative Hypotheses
The following null and alternative hypotheses need to be tested:
H0?: The high motivation and high talent are independent
Ha?: The high motivation and high talent
Assume alpha =0.05
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