Question
Asked Nov 26, 2019
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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.
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Expert Answer

Step 1

Given:

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

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Step 2

(a)

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

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Step 3

(b)

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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