In the following problem, check that it is appropriate to use the normal approximation to the binomial. Then use the normal distribution to estimate the requested probabilities. Do you take the free samples offered in supermarkets? About 60% of all customers will take free samples. Furthermore, of those who take the free samples, about 35% will buy what they have sampled. Suppose you set up a counter in a supermarket offering free samples of a new product. The day you were offering free samples, 325 customers passed by your counter.

a) what is the probability that more than 180 will take your free sample?

b) what is the probability that fewer than 200 will take your free sample?

c) what is the probability that between 60 and 80 customers will take the free sample and buy the product?