Hello, I must show work so please provide how you came up with answer. Are custo

Question

Hello,

I must show work so please provide how you came up with answer.

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 reglons of the United States. s 5-9 Years 10-14 Years 15 or More Years Row Total 154 Midwest South 21 53 70 65 69 93 120 158 63 106 Column Total 157 287 469 291570 What is the probability that a customer chosen at random has the following characteistics? (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, glven 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 is from the South, given that he or she has been loya less than 1 year g) has bean loyal 1 or more ysars, given that he or sha is from the Fast has been loyal 1 or mara yoara, given that he or sha is from tha Wast i Are the events fram the East and layal 15 or more years indopendent? Explain O No. These events cannot occur together Yes. These events can occur together No. Ployal 15 o more years) Ploya 15 o more years | East). O Yes. P loyal 15 or more years)P(loyal 15 or more years East).

Explanation / Answer

a)

P(loyal for 10-14) =291/2031 (As 291 people who are loyal out of total 2031 people)

b)P(loyal for 10-14|east) =77/463 (as 77 people who are loyal out of total 463 people from east)

c)P(at least 10 years) =(291+570)/2031=861/2031 (as 861 people of 10 or more years who are loyal out of 2031)

d)P(at least 10 years given west)=(45+92)/384 =137/384

e)P(west|less than 1 year)=41/157 ( as 41 people from west out of 157 who are loyal for less than 1 year)

f)P(south |less than 1 year)=53/157

g)P(loyal for 1 or more years|east)=(463-32)/463=431/463

h)P(loyal for 1 or more years|west)=(384-41)/384=343/384

i)No P(loyal 15 or more years ) is not equal to  P(loyal 15 or more years|east )

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