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.

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

Less Than 1 Year 1-2 Years 3-4 Years 5-9 Years 10-14 Years 15 or More Years Row Total East 32 38 59 112 77 102 420 Midwest 31 56 68 120 63 179 517 South 53 98 93 158 106 193 701 West 41 71 67 78 45 62 364 Column Total 157 263 287 468 291 536 2002

Explanation / Answer

Solution:

total number of customers = 2002

(a)

probability that the customer  has been loyal 10 to 14 years = 291 / 2002 = 0.1453

(b)

probability that the customer has been loyal 10 to 14 years, given that he or she is from the East = 77/420 = 0.1833

(c)

probability that the customer has been loyal at least 10 years = ( 291+536)/2002 = 0.4130

(d)

probability that the customer  has been loyal at least 10 years, given that he or she is from the West = (45+62)/364

= 0.2939

(e)

probability that the customer  is from the West, given that he or she has been loyal less than 1 year = 41/157

= 0.2611

(f)

probability that the customer is from the South, given that he or she has been loyal less than 1 year = 53/157

= 0.3375

(g)

probability that the customer has been loyal 1 or more years, given that he or she is from the East

= ( 38+59+112+77+102 ) /420

= 0.9238

(h)

probability that the customer has been loyal 1 or more years, given that he or she is from the West

= ( 71+67+78+45+62)/364

= 0.8873

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