Are customers more loyal in the East or in the West? The following table is base
ID: 3128726 • 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.
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.
No. These events cannot occur together. No. P(loyal 15 or more years) P(loyal 15 or more years | East). Yes. P(loyal 15 or more years) = P(loyal 15 or more years | East). Yes. These events can occur together.
Less Than 1 Year 1-2 Years 3-4 Years 5-9 Years 10-14 Years 15 or More Years Row Total East 32 58 59 112 77 147 485 Midwest 31 41 68 120 63 181 504 South 53 104 93 158 106 161 675 West 41 40 67 78 45 99 370 Column Total 157 243 287 468 291 588 2034Explanation / Answer
A. 291/2034=0.143
B.P(A|b)=P(A and B)/P(B)=(77/2034)/(485/2034)=0.158
C.(291+588)/2034=0.432
D.P(A|b)=P(A and B)/P(B)=(45+99)/370=0.389
E.41/157=0.262
F.53/157=0.337
G.(58+59+112+77+147)/485=0.934
99)/ 370=0.889
I. No they are not independent
as P( a and b)=147/2034
P(A)=485/2034
P(B)=588/2034
for events to be independent P(A).P(B)=P(A and b) which is not the case above
H. (40 +67+ 78+ 45+99)/ 370=0.889
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