Are customers more loyal in the East or in the west? The following table is base
ID: 3023723 • Letter: A
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 loyaltiy 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? has been loyal 10 to 14 years has been loyal to 14 years, given that he or she is from the East has been loyal at least 10 years, given that he or she is from the west is from the west, given that he or she has been loyal less than 1 year is from the south, given that he or she has been loyal less than 1 year has been loyal 1 or more years, given that he or she is from the East.has been loyal 1 or more years, given that he or she is from the west.Explanation / Answer
(a) Probability that a customer chosen at random has been loyal 10-14 years
=P(customer loyal for 10-14 years) = 291/2028=97/676
(b) Probability that a customer chosen at random has been loyal 10-14 years, given that he or she is from the East
= P( customer loyal for 10-14 years | he or she from the East) = 77/467
(c) Probability that a customer chosen at random has been loyal at least10 years
= P(customer loyal for atleast 10 years) = (291+558)/2028 = 283/676
(d) Probability that a customer chosen at random has been loyal at least 10 years, given that he or she is from the West
=P(customer loyal atleast 10 years | he or she from West)= (45+92)/383 =137/383
(e) Probability that a customer chosen at random is from the West, given that he or she has been loyal less than 1 year
= P(customer from West | he or she is loyal less than 1 year) = 41/157
(f) Probability that a customer chosen at random is from the South, given that he or she has been loyal less than 1 year
= P(customer from South | he or she is loyal less than 1 year) = 53/157
(g) Probability that a customer chosen at random has been loyal 1 or more years, given that he or she is from the East
= P(customer is loyal more than 1 year | he or she is from East) = (467-32)/467 = 435/467
(h) Probability that a customer chosen at random has been loyal 1 or more years, given that he or she is from the West
=P(customer is loyal more than 1 year | he or she is from West) = (383-41)/383 = 342/383
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