Question

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?

Answer 1

Answer: 0.9171

Explanation:

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

`P(x)= ^nC_xp^x(1-p)^(n-x)`, 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 :-

`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`

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