columns represent length of cusl market. The rows represent regions of tl 14 15
ID: 3330537 • Letter: C
Question
columns represent length of cusl market. The rows represent regions of tl 14 15 or More 1 Year Years Years Years Years 54 59112 Row Total YearsTo Less Than 1-2 3-4 5-9 10 118 173 158 86 535 32 53 92 93 158 106 45 East Midwest31 68 68120 63 373 41 56 67 78 468 291 West 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 (c) has been loyal at least 10 years? d) has been loyal at least 10 years, given that he or she is fro Colme Total 157 270 287 iven that he or she has been loyal less than 1 year? n I year? (g) has been loyal I or more years, given that he or she is from the east? (e) is from the west, 0) is from the south, given that he or she has been loyal less than vea is from the south, given thExplanation / Answer
Question 32:
a) Probability that a customer has been loyal 10 to 14 years is computed as:
= Total number of customers that has been loyal 10 to 14 years / Total frequency
= 291 / 2008
= 0.1449
Therefore 0.1449 is the required probability here.
b) Probability that the customer has been loyal 10 to 14 years, given that he or she is from east is computed using bayes theorem as:
= Total number of customers that has been loyal 10 to 14 years from east / Total customers from east
= 77 / 452
= 0.1704
Therefore 0.1704 is the required probability here.
c) Now probability that the customer has been loyal at least 10 years is computed as:
= Total number of customers that are loyal for at least 10 years / Total frequency
= ( 291 + 535 ) / 2008
= 0.4114
Therefore 0.4114 is the required probability here.
d) Probability that the customer has been loyal at least 10 years, given that the customer is from west is computed as:
= Total number of customers that are loyal for at least 10 years from west / Total frequency from west
= ( 45 + 86 ) / 373
= 0.3512
Therefore 0.3512 is the required probability here.
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