Solve the problem of example 2.6 (page 54) by making use of the normal approximation to the hypergeometric distribution and compare with the exact result.

Data from Example 2.6

A customer knows that on average 4% of parts delivered by a manufacturer are defective and has accepted this percentage. To check whether the manufacturer exceeds this limit, the customer takes from each batch of 800 parts randomly a sample of size 80 and accepts the delivery if there are at most 3 defective parts in a sample. What is the probability that the customer accepts a batch, which contains 50 defective parts, although it should be on average only 32 defective parts?