SG#14 Are customers more loyal in the East or in the West? The following table i
ID: 2908952 • Letter: S
Question
SG#14
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. P(loyal 15 or more years) ? P(loyal 15 or more years | East).Yes. These events can occur together. Yes. P(loyal 15 or more years) = P(loyal 15 or more years | East).No. These events cannot 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 36 59 112 77 108 424 Midwest 31 47 68 120 63 178 507 South 53 107 93 158 106 205 722 West 41 32 67 78 45 71 334 Column Total 157 222 287 468 291 562 1987Explanation / Answer
Probabaility = number of favourable event / total number of event
a) has been loyal 10 to 14 years
= 291/1987
here total = 1987 and number of people who are loyal in 1014 years = 291
hence 291/1987
(b) has been loyal 10 to 14 years, given that he or she is from the East
P(A |B) = P(A and B)/P(B)
= 77/424
(c) has been loyal at least 10 years
=(291 + 562)/1987
= 853/1987
(d) has been loyal at least 10 years, given that he or she is from the West
=(45+71)/334
=126/334
(e) is from the West, given that he or she has been loyal less than 1 year
=41/157
(f) is from the South, given that he or she has been loyal less than 1 year
=53/157
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