score: 0 of 6 pts | 8 of 10 (7 complete) 5.3.29-T and mi Selected consumers. Com

Question

score: 0 of 6 pts | 8 of 10 (7 complete) 5.3.29-T and mi Selected consumers. Complete arts hrought d A brand name has a 50% reco n on rate Assume the o ner o he brand wants to verif hat rate by beginning a. What is the probability that exactly 7 of the selected consumers recognize the brand name? The probability that exactly 7 of the 8 consumers recognize the brand name is 0.031 ith a small sample of e ow Round to three decimal places as needed.) b. What is the probability that all of the selected consumers recognize the brand name? The probability that all of the selected consumers recognize the brand name is (Round to three decimal places as needed)

Explanation / Answer

a)

Proportion(p) = 0.5

n = 8

Mean(µ) = p = 0.5

Std Deviation () = sqrt((p*(1-p))/n) = 0.177

X = 7/8 = .875

Z = (x- µ)/ = (.875-.5)/0.177 = 2.12

P(x<=7) = P(z<=2.12) = .9830 (from z-table)

X1 = 6/8 = 0.75

Z1 = (.75-.5)/0.177 = 1.41

P(x<=6) = P(z<=1.41) = 0.9207

Hence,

P(x=7) = P(x<=7) – P(x<=6) = 0.9830 – 0.9207 = 0.0623 or 6.23%

b)

x = 8/8 = 1

Z2 = (1-.5)/0.177 = 2.83

P(x<=8) = P(z<=2.83) = 0.9977

Hence,

P(x=8) = P(x<=8) – P(x<=7) = 0.9977-0.9830 = 0.0147 or 1.47%

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