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	56	59	112	77	121	457
Midwest	31	58	68	120	63	181	521
South	53	112	93	158	106	184	706
West	41	44	67	78	45	98	373
Column Total	157	270	287	468	291	584	2057

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.

No. These events cannot occur together.No. P(loyal 15 or more years) ≠ P(loyal 15 or more years | East).    Yes. These events can occur together.Yes. P(loyal 15 or more years) = P(loyal 15 or more years | East).

Based on data from a statistical abstract, only about 20% of senior citizens (65 years old or older) get the flu each year. However, about 28% of the people under 65 years old get the flu each year. In the general population, there are 12% senior citizens (65 years old or older). (Round your answers to three decimal places.)

(a) What is the probability that a person selected at random from the general population is senior citizen who will get the flu this season?


(b) What is the probability that a person selected at random from the general population is a person under age 65 who will get the flu this year?


(c) Repeat parts (a) and (b) for a community that has 93% senior citizens.

(a)
(b)

(d) Repeat parts (a) and (b) for a community that has 48% senior citizens.

(a)
(b)

Answer 1

Note : Allowed to solved only 4 sub question in one post.

(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

P(customer loyal for 10 to 14 years|customer from the East) =

P(customer loyal for 10 to 14 years|customer 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

P(Customer loyal for at least 10 years | Custmer from the west) =

P(Customer loyal for at least 10 years | Customer from the west) =