Asked Nov 26, 2019
Thirty percent of consumers prefer to purchase electronics online. You randomly select 8consumers. Find the probability that the number of consumers who prefer to purchase electronics online is​ (a) exactly​ five, (b) more than​ five, and​ (c) at most five.

Expert Answer

Step 1


Probability of success (p) = 0.30

Number of trials (n) = 8

Consider, X be the random variable that represents the number of consumers who prefer to purchase electronics online is binomially distributed with the parameters n= 8 and p = 0.30, that is,


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Bin(n 8,p= 0.30) X

Step 2


The probability that the number of consumers who prefer to purchase electronics online is exactly​ 5 can be computed as:


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P(X 5)C, x(0.30) x(1-0.30)* =0.047

Step 3


The probability that the number of consumers who prefer to purch...


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P(X>5)= P(X 6)+ P(X = 7)+ P(X = 8) ($Cx(0.30)* x (1-0.30)* $C(0.30)x(1-0.30)* C, x(0.30)' x(1-0.30) =0.011


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