Are customers more loyal in the East or in the West? The following table is base

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 41 157 9 Years 10-14 Years 15 or More Years Row Total 438 East Midwes South West Column Total 42 70 79 76 267 59 68 93 67 287 112 120 158 78 468 147 197 63 106 45 291 686 373 1996 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 (t) 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

Explanation / Answer

a) Total customers = 1996

Total loyal in 10 - 14 = 291

Probability = 291/1996

b) This is a conditional probabilty

Probability = 77/438

c) at least 10 years would contain 10-14 and greater than 15

Probability = (291 + 526)/1996 = 817/1996

d)

Probability = (45+ 66)/373 = 111/373

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