Question: A binomial experiment consists of 500 trials with the probability of success for each trial .4. What is the probability of obtaining the number of successes indicated? Approximate these probabilities to two decimal places using a normal curve. (This binomial experiment easily passes the rule-of-thumb test, as you can check. When computing the probabilities, adjust the intervals as in Examples I and II.)
EXAMPLE I: Market Research A credit card company claims that their card is used by 40% of the people buying gasoline in a particular city. A random sample of 20 gasoline purchasers is made. If the company's claim is correct, what is the probability that
(A) From 6 to 12 people in the sample use the card?
(B) Fewer than 4 people in the sample use the card?
EXAMPLE II: Quality Control A company manufactures 50,000 ballpoint pens each day. The manufacturing process produces 50 defective pens per 1,000, on the average. A random sample of 400 pens is selected from each day's production and tested. What is the probability that the sample contains
(A) At least 14 and no more than 25 defective pens?
(B) 33 or more defective pens?