Question

A popular online retailer sells a wide variety of products including books. The proportion of customers that order only books is 21%. If a random sample of 600 customers is taken, what is the probability that more than 24% order only books?

Answer 1

Use the normal approximation to the binomial distribution.

First find mean and standard deviation.

mean = np = (600)(.21) = ?
standard deviation = √npq = √(600)(.21)(.79) = ?
Note: q = 1 - p

I'll let you finish the calculations.

Next take .24 times 600. Use that value for x in the z-score equation:
z = (x - mean)/sd

Once you calculate the z-score, look at a z-table to determine the probability. Remember that the problem is asking "more than" when you check the table.

I hope this will help get you started.

Answer 2

0.983