ACNielsen is a New Yorkbased corporation and a member of the

ACNielsen is a New York-based corporation and a member of the
modern marketing research industry.
One of the items that ACNielsen tracks is the expenditure on over-the-counter (OTC)
cough medicines. ACNielsen recently indicated that consumers spent $620 million on
GTC cough medicines in the United States. The article also indicated that nearly 30
million visits for coughs were made to doctors\' offices in the United States.
a. Determine the average cost of OTC cough medicines per doctor\'s office visit based on
30 million purchases.
b. Assuming that the average cost indicated in part a is the true average cost of GTC
cough medicines per doctor\'s visit and the standard deviation is $10, determine the
probability that the average cost for a random selection of 30 individuals will result in an average expenditure of more than $25 in OTC cough medicines.
c. Determine the 90th percentile for the average cost of OTC cough medicines for a
sampleof 36 individuals,

Solution

(a) average = 620000000/30000000 = 20.66667

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(b) So the probability is

P(xbar>25) = P((xbar-mu)/(s/vn) >(25-20.66667)/(10/sqrt(30)))

=P(Z>2.37) = 0.0089 (from standard normal table)

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(c) P(xbar <x) = 0.9

--> P((xbar-mu)/(s/vn) <(x-20.66667)/(10/sqrt(36))) =0.9

--> P(Z<(x-20.66667)/(10/sqrt(36)))= 0.9

--> (x-20.66667)/(10/sqrt(36)) = 1.28 (from standard normal table)

--> x= 20.66667 +1.28*(10/sqrt(36)) =22.8