Posted by **Jason L** on Monday, February 26, 2007 at 3:23pm.

A paper manufacturer claims that fewer than 1 in 100 of its reels (2 ton rolls) of paper is flawed. A customer has just received a large shipment of these reels and proceeds to check a random sample of 600 of them for flaws. Of this sample, 14 reels are found to be flawed. What is the probability of finding at least 14 flawed reels in this sample?

You can use the normal approximation to the binomial distribution.

Your values are the following:

p = 1/100 = .01, q = 1 - p = 99/100 = .99, x = 14, and n = 600

You need to find mean and standard deviation.

mean = np = (600)(.01) = 6

standard deviation = √npq = 2.44 (this is a rounded value)

Now use z-scores to find probability:

z = (x - mean)/sd -->sd = standard deviation

With your data:

z = (14 - 6)/(2.44) = 3.28

Using a z-table, you will find the probability to be very small.

I hope this will help.