posted by Jacob on .
Assume that about 45% of all U.S. adults try to pad their insurance claims. Suppose that you are the director of an insurance adjustment office. Your office has just received 110 insurance claims to be processed in the next few days. What is the probability that fewer than 45 of the claims have been padded?
Using the normal approximation to the binomial distribution, find the mean and standard deviation, then use z-scores to find your probability.
Your values are the following:
p = .45, q = 1 - p = .55, x = 45, and n = 110
Now find mean and standard deviation.
mean = np = (110)(.45) = ?
standard deviation = √npq = √(110)(.45)(.55) = √(27.225) = ?
Once you have finished the calculations, then use z-scores and z-table to find probability:
z = (x - mean)/sd
Once you have the z-score, then use the table to determine your probability. Remember the problem is asking "fewer than" when looking at the table to determine your probability. You should find the answer you seek from the choices given.
I hope this will help get you started.