1. Suppose 30% of MU students watch reality TV shows of some kind every week. Three MU students are selected at random and asked if they watch reality TV of some kind each week. Let X be the number of students in the sample who answer YES. Find the probability distribution for X using two methods: 1) use the formulas and work it out; AND 2) use the binomial table and calculate from there. (Remember what a probability distribution means see notes from discrete random variables.) USING F ORMU LAS: 2. Explain why X DOES NOT have a binomial distribution in each of the situations below. (Hint, check the criteria; if you nd one that isn't met, X isn't binomial.) a. Suppose a police ofcer takes a two-hour time period and records the number of vehicles traveling on US 131 that exceed the speed limit (where the speed limit is 70 miles per hour). Let X denote the number of vehicles that were exceeding the limit. . Suppose 10% of OSU business students major in international marketing. You keep sampling students at random from our class until you nd someone who is majoring in international marketing. Let X = the number of students you have to sample. You have 10 people working for you, 5 men and 5 women, and you have to choose different people be on a committee that no one wants to be on. You put their names into a hat and pull out 3 names, one by one. Let X = number of women who end up on the committee. . You take a random sample of 10 college students from stat 1430 and record their status (freshman, sophomore, etc.). Suppose a police ofcer takes a two-hour time period and records the number of vehicles traveling on US 131 that exceed the speed limit (where the speed limit is 70 miles per hour). Let X denote the number of vehicles that were exceeding the limit. Explain why X does NOT have a binomial distribution. 3. Which of the following has a Binomial distribution? a. The number of customers arriving at a gas station on July 4 b. The number of people against a smoking ban out of a random sample of 100. c. The number of telephone calls received by a switchboard in a specied time period d. All of the above have a binomial distribution. 4. One out of four of the students in an English class is an international student. Take a random sample of 100 students from this class and let X = the number of international students. The mean of X is what? (Note! You are not given p directly but you can nd it): a. 18.75 b. 4.33 c. 25 d. 5 . 30% of MU students have cars that are black. Suppose you randomly sample 5 MU students, and let X be the number of students in the sample with black cars. Find the probabilities of the following events. a. Exactly 3 students in the sample have black cars. . More than 3 students in the sample have black cars. . Less than half of the students in the sample have black cars. . At least one student in the sample has a black car. Suppose you ip a fair coin 7 times, and let X be the total number of tails. What is the probability that X is greater than 1? (Hint, what is p when you ip a fair coin?) . 6. Suppose X is binomial withp = .90. What does n have to be (at a minimum) to use the normal approximation for X? 7. Suppose a media report claims that 25% of children are addicted to video games. You think the percentage is higher than that. You take a random sample of 200 children and nd that at least 70 of them are addicted to video games. a. What is the chance of this result happening? b. Based on your results do you believe the claim that 25% of children are addicted to video games? Why or why not? 8. The national proportion of adults who are concerned about nutrition is 0.35. You take a random sample of 5 adults and count the number who are concerned about nutrition (call this number X). . What is 1.1x? . What is 6,? . What is P(X = 3)? . What is the probability that X is at most 3? (Use the table) What's the probability that X is at least 3? (Use the table) Explain why the previous two problems are NOT complements of each other