Say we have a random sample of n = 15 online customers from a large population of customers to a popular online auction site. With p = 0.07 of the population proportion making a purchase, what is the probability of selecting exactly two customers who actually make a purchase in the random sample?

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28-08-2019
Mathematics

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Say we have a random sample of n = 15 online customers from a large population of customers to a popular online auction site. With p = 0.07 of the population proportion making a purchase, what is the probability of selecting exactly two customers who actually make a purchase in the random sample?

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JeanaShupp JeanaShupp · Answer 1 · 2019-09-02T09:17:44+02:00

Answer: 0.9171

Step-by-step explanation:

Binomial distribution formula to find the probability of success in x trials:-

[tex]P(x)= ^nC_xp^x(1-p)^{n-x}[/tex], where n is the sample size and p is the population proportion for each trial.

Given : n= 15 ; p= 0.07

Then , the customers who actually make a purchase in the random sample is given by :-

[tex]P(x=2)=P(0)+P(1)+P(2)\\\\=^{15}C_{0}(0.07)^0(0.93)^{15}+^{15}C_{1}(0.07)^1(0.93)^{14}+^{15}C_{2}(0.07)^2(0.93)^{13}\\\\=(0.93)^{15}+(15)(0.07)^1(0.93)^{14}+105(0.07)^2(0.93)^{13}\\\\=0.9171390460254\approx0.9171[/tex]

Hence, the probability of selecting exactly two customers who actually make a purchase in the random sample = 0.9171