# In the following problem check that it is appropriate to use

Last updated: 2/1/2024

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 58 of all customers will take free samples Furthermore of those who take the free samples about 39 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 309 customers passed by your counter Round your answers to four decimal places USE SALT 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 a customer will take a free sample and buy the product Hint Use the multiplication rule for dependent events Notice that we are given the conditional probability P buy sample 0 39 while P sample 0 58 0 2262 d What is the probability that between 60 and 80 customers will take the free sample and buy the product Hint Use the probability of success calculated in part c