1. The manager of Sam's Food Mart guarantees that none of his cartons containing a dozen eggs will contain more than one bad egg, despite the fact that 2% of individual eggs are known to be bad. Define the random variable x to be the number of bad eggs observed in a carton containing 12 eggs.

a) Explain why this experiment can be classified as a binomial experiment. Give two specific reasons.

It gives you the error of margin (2%) and tells you the sample.

b) Find the probability that a randomly selected carton will contain no bad eggs.

c) If a carton contains more than one bad egg, the manager will replace the entire dozen and allow the customer to keep the original eggs. Find the probability that the manager will have to replace a randomly selected carton of eggs.

2. At Express Delivery Service, providing high-quality service to its customers is the top priority of management. The company guarantees a refund of charges if a package it is delivering does not arrive to its destination on time.  Despite all efforts, 94% of the packages mailed through the company arrive at their destinations on time. A Corporation mailed seven packages through Express Delivery on Monday.

a) Find the probability that all of the seven packages will arrive on time.

b) Find the probability that exactly two of these seven packages will not arrive on time.

c) Interpret the meaning of your answer to part b.