Question

Say we have random sample n = 15 online customers large population customers 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

Given:

Random sample n = 15 online customers large population customers popular online auction site.

Probability of making a purchase, p = 0.07.

To Find:

The probability of selecting exactly two customers who actually make a purchase in the random sample.

Solution:

We have total number of customers = 15.

Number of customers who made a purchase = 2

Probability of making a purchase = 0.07

This is a Bernoulli Process.

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

• P = $nC_k p^{k} (1-p)^{n-k}$
• P = 15$C_2$ (0.07)²($0.93^{13}$)
• P = 105 x 0.0049 x 0.39
• P =  0.2

The probability of selecting exactly two customers who actually make a purchase in the random sample is 0.2.