Are customers more loyal in the East or in the West? The following table is base
ID: 3052880 • Letter: A
Question
Are customers more loyal in the East or in the West? The following table is based on information from a recent study. The columns represent length of customer loyalty (in years) at a primary supermarket. The rows represent regions of the United States.
Less Than 1 Year
1-2 Years
3-4 Years
5-9 Years
10-14 Years
15 or More Years
Row Total
East
32
62
59
112
77
121
463
Midwest
31
70
68
120
63
154
506
South
53
65
93
158
106
203
678
West
41
61
67
78
45
92
384
Column Total
157
258
287
468
291
570
2031
What is the probability that a customer chosen at random has the following characteristics? (Enter your answers as fractions.)
(a) has been loyal 10 to 14 years
(b) has been loyal 10 to 14 years, given that he or she is from the East
(c) has been loyal at least 10 years
(d) has been loyal at least 10 years, given that he or she is from the West
(e) is from the West, given that he or she has been loyal less than 1 year
(f) is from the South, given that he or she has been loyal less than 1 year
(g) has been loyal 1 or more years, given that he or she is from the East
(h) has been loyal 1 or more years, given that he or she is from the West
(i) Are the events from the East and loyal 15 or more years independent? Explain.
Less Than 1 Year
1-2 Years
3-4 Years
5-9 Years
10-14 Years
15 or More Years
Row Total
East
32
62
59
112
77
121
463
Midwest
31
70
68
120
63
154
506
South
53
65
93
158
106
203
678
West
41
61
67
78
45
92
384
Column Total
157
258
287
468
291
570
2031
Explanation / Answer
a)P( loyal 10 to 14 years) =291/2031
b)P( loyal 10 to 14 years|East)=77/463
c) P( loyal at least 10 years) =(291+570)/2031=861/2031
d)
P( loyal at least 10 years, given that he or she is from the West) =(45+92)/384=137/384
e)P(is from the West, given that he or she has been loyal less than 1 year)=41/157
f)P is from the South, given that he or she has been loyal less than 1 year) =53/157
g)Phas been loyal 1 or more years, given that he or she is from the East)=(463-32)/463=431/463
h)P(has been loyal 1 or more years, given that he or she is from the West) =(384-41)/384 =343/384
i)here P(from east and loyal 15 or more years)=121/2031 =0.0596
which is not equal to P(from east)*P( loyal 15 or more years) =(570/2031)*(463/2031) =0.0640
hence events from east and loyal 15 or more years are not independent
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