Are customers more loyal in the East or in the West? The following table is base
ID: 3265300 • 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 32 31 53 1-2 Years 42 70 79 76 267 3-4 Years 59 68 93 67 287 5-9 Years 112 120 158 78 468 Row Total 438 499 686 373 1996 10-14 Years East Midwest South West Column Total 63 106 45 291 15 or More Years 116 147 197 157 526 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 WestExplanation / Answer
Answer with details below:
Concept1: Beware when conditional probability is asked or when simple probability is being asked.Both are different
a. has been loyal 10 to 14 years = 291/1996 = .1458
b. has been loyal 10 to 14 years given he' from East = 77/291 = .2646
c. has been loyal alteast 10 years = (291+526)/1996 = .4093
d. has been loyal atleast 10 years, given he' from West = (45+66)/373 = .2976
e. is from West given loyalty less than 1 year = 41/157 = .2611
g. has been loyal 1 or more than 1 year. given he' from East = 406/438 = .9269
h. has been loyalty 1 or more than 1 year, given he from West = 332/373 = .8900
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