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 1-2 Years 3-4 Years 5-9 Years 10-14 Years 15 or More Years Row Total East 32 70 59 112 77 138 488 Midwest 31 43 68 120 63 150 475 South 53 67 93 158 106 202 679 West 41 63 67 78 45 61 355 Column Total 157 243 287 468 291 551 1997 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. Yes. P(loyal 15 or more years) = P(loyal 15 or more years | East). No. These events cannot occur together. Yes. These events can occur together. No. P(loyal 15 or more years) ≠ P(loyal 15 or more years | East).

Answer 1

a)P(has been loyal 10 to 14 years) =291/1997=					291/1997
b)P(has been loyal 10 to 14 years|east) =77/488=					77/488
c)P(has been loyal at least 10 years) =					842/1997
d)P(has been loyal at least 10 years given west) =					106/355
e)P(west given loyal less than 1 years) =					41/157
f)P(south given loyal less than 1 years) =					53/157
g)P(has been loyal 1 or more years given from east) =456/488=					57/61
h)P(has been loyal 1 or more years given from west) =					314/355

No. P(loyal 15 or more years) ≠ P(loyal 15 or more years | East).