Steele Electronics, Inc sells expensive brands of stereo equipment in several sh

Question

Steele Electronics, Inc sells expensive brands of stereo equipment in several shopping malls throughout the northwest section of the United States. The Marketing Research Department of Steele reports that 30 percent of the customers entering the store that indicate they are browsing will, in the end, make a purchase. Let the last 15 customers who enter the store be a sample.

a. what is the probability that exactly five of these customers make a purchase?

b. What is the probability seven or more make a purchase?

c. Does it seem likely at least one will make a purchase?

Explanation / Answer

percent of the customers entering the store that indicate they are browsing will, in the end, make a purchase = 30%

P(customers entering the store that indicate they are browsing will, in the end, make a purchase) i.e p= 0.3

P(customers entering the store that indicate they are browsing will, in the end, not make a purchase) = 1-p = 1-0.3 = 0.7

sample size i.e n = 15

no of ways to select r objects from n objects = nCr = n!/(r!*(n-r)!)

a)

probability that exactly five of these customers make a purchase = (15C5)(0.3)5(0.7)10 = 0.2061

b)

probability seven or more make a purchase = P(7)+P(8)+P(9)+P(10)+P(11)+P(12)+P(13)+P(14)+P(15)

=  (15C7)(0.3)7(0.7)8+ (15C8)(0.3)8(0.7)7+ (15C9)(0.3)9(0.7)6+ (15C10)(0.3)10(0.7)5+ (15C11)(0.3)11(0.7)4+ (15C12)(0.3)12(0.7)3++ (15C13)(0.3)13(0.7)2+ (15C14)(0.3)14(0.7)1+(15C15)(0.3)15(0.7)0 = 0.1311

c)

probability that at least one will make a purchase = 1 - 0.715 = 0.9952

so it is likely that at least one will make a purchase

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