Show your work or explain how you arrived at your conclusion whenever appropriate. 1. In 2008 the stock market crashed. During this time, a survey of adult investors were asked how often they tracked their portfolio. The table below shows the investors responses. Find the probability that an adult investor does not track his or her own portfolio. (8 points) How frequently? Daily Weekly Monthly Couple of times a year Don't Track 2. Response 240 283 280 141 49 The table lists the smoking habits of a group of college students. (20 points) Gender Male Female Total Non-smoker 130 185 315 Regular Smoker 46 20 66 Heavy Smoker 5 4 9 Total 181 209 390 a) If a student is chosen at random, find the probability of getting someone who is a nonsmoker. Round your answer to three decimal places. (5 points) b) If a student is chosen at random, find the probability of getting someone who is a regular or heavy smoker. Round your answer to three decimal places. (5 points) c) If a student is chosen at random, find the probability of getting someone who is a female or a non-smoker. Round your answer to three decimal places. (5 points) d) If a student is chosen at random, find the probability of getting someone who is a male or female. Round your answer to three decimal places. (5 points) 3. A golden retriever has three puppies in a litter. The random variable X represents the number of female puppies born in the litter. Construct the probability distribution for the random variable X in the table below. (8 points) X P(X) 4. 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. (22 points) a) Explain why this experiment can be classified as a binomial experiment. Give two specific reasons. (6 points) b) Find the probability that a randomly selected carton will contain no bad eggs. (8 points) 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. (8 points) c) 5. 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. (22 points) a) Find the probability that all of the seven packages will arrive on time. (8 points) b) Find the probability that exactly two of these seven packages will not arrive on time. (8 point c) Interpret the meaning of your answer to part b. (6 points)