Survey: Customer Loyalty Are customers more loyal in the east or in the west? The following table is based on information from Trends in the United States, published by the Food Marketing Institute, Washington, D.C. 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 54 59 112 77 118 452 Midwest 31 68 68 120 63 173 523 South 53 92 93 158 106 158 660 West 41 56 67 78 45 86 373 Column Total 157 270 287 468 291 535 2008 What is the probability that a customer chosen at random

(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.

AppendixLO1