Question

Suppose the likelihood that someone who logs onto a particular site in a "shopping mall" on the Internet will purchase an item is 0.10. If the site has 200 people accessing it in the next day, what is the probability that less than 24 customers will make a purchase?

A. 0.5

B. 0.1736

C. 0.8264

D. 0.2561

Answer 1

Solution:

Given: Suppose the likelihood that someone who logs onto a particular site in a "shopping mall" on the Internet will purchase an item is 0.10. That is: p = 0.10

n = sample size = 200

We have to find: the probability that less than 24 customers will make a purchase.

P( X < 24) =.......?

Since sample size n = 200 is large, we use Normal approximation to Binomial.

Mean :

Standard Deviation :

Thus find z score:

Thus we get:

P( X < 24) =P( Z< 0.94)

Look in z table for z = 0.9 and 0.04 and find area.

P( Z< 0.94)= 0.8264

Thus

P( X < 24) =P( Z< 0.94)

P( X < 24) = 0.8264