1. Normal Approximation 1

2 Suppose we perform a sequence of n binomial trials with probability of success p and probability of failure q = 1 - p and observe the number of successes. Then the histogram for the resulting probability distribution may be approximated by the normal curve with = np and

 Binomial distribution with n = 40 and p =.3 3

4 A plumbing-supplies manufacturer produces faucet washers that are packaged in boxes of 300. Quality control studies have shown that 2% of the washers are defective. What is the probability that more than 10 of the washers in a single box are defective?

5 Let X = the number of defective washers in a box. X is a binomial random variable with n = 300 and p =.02. We will use the approximating normal curve with = 300(.02) = 6 and Since the right boundary of the X = 10 rectangle is 10.5, we are looking for Pr(X > 10.5).

6 The area of the region to the right of 1.85 is 1 - A(1.85) = = Therefore, 3.22% of the boxes should contain more than 10 defective washers.

 Probabilities associated with a binomial random variable with parameters n and p can be approximated with a normal curve having = np and 7