Name: Instructor: A.E.Cary Instructions: Show all your work in a manner consistent with that demonstrated in class. Round your answers where appropriate. Use 3 decimal places when rounding answers. In most cases, your answer should be stated using a complete sentence. The entire exam is closed-note, closed-book. You may use your calculator and Excel throughout the entire exam. You may also use the formula sheet provided to you. Wherever you use Excel or your calculator, make sure that any calculations you do are clearly included in your work. 1. For each scenario, identify the type of sample used. Possible choices include: census, SRS, stratefied, systematic, cluster, multistage, voluntary, and convenience. If you answer multistage, list the multiple sample types. Not all of these will be used; it s possible that you could use one more than once. Scenario Sample Type An online poll asks participants what their favorite type of ice cream is. At the von Trapp family reunion, there are 114 attendees. They use a random number generator to select a sample of 10 to participate in a game of tug-of-war. There are 30 sections of MTH 243 at PCC this term. Eight sections are chosen at random and every student in those sections is surveyed. PCC randomly selects 100 male students and 100 female students to survey about their thoughts on the cafeteria food at PCC. 2. A household reviews their gas and electricity bills for 12 months from a given year. They notice that whenever their electricity bill is higher, their gas bill is also higher. If all 12 months support this statement, can they conclude that higher electric bills cause higher gas bills? Justify your answer. [8 points; 4 points]
3. Suppose the chance that it rains on a given day in July in Portland is 6%. Assume that day-to-day July weather is considered independent. (a) What s the probability that it does NOT rain for 5 days in a row in July? (b) What s the probability that it does NOT rain for 2 days and then rains on the third day over a 3-day period in July? (c) What s the probability that it rains at least once in a 4-day period in July? [4 points, 4 points, 4 points] Instructor: A.E.Cary Page 2 of 8
4. Record the sample space for each of the following. (a) Roll one die and toss one coin. Record the number on the die and whether the coin shows heads or tails. (b) Roll two dice. Record the sum of the numbers. 5. A jar contains 95 pieces of candy. There are 25 yellow candies, 32 pink candies, and 38 green candies. (a) You draw one piece of candy from the jar. What s the probability this it is green or yellow? (b) You draw three pieces of candy. What s the probability that NONE of them are yellow? Hint: Visualize drawing these one at at time! [2 points, 2 points; 4 points, 4 points] Instructor: A.E.Cary Page 3 of 8
6. In our MTH 243 class, assume that 85% like chocolate, 70% like popcorn, and 68% like both chocolate and popcorn. (a) Draw a Venn diagram representing this scenario. (b) What s the probability that a randomly selected student likes either chocolate or popcorn? (c) What s the probability that a randomly selected student likes chocolate given that they do NOT like popcorn? [4 points, 4 points, 4 points] Instructor: A.E.Cary Page 4 of 8
7. An ultrasound machine is used by a radiologist to predict the gender of a sample of babies. Of this sample, 52.5% are born male and 47.5% are born female. Of those born male, 88% were correctly predicted as male in the ultrasound. Of those born female, 84% were correctly predicted as female in the ultrasound. (a) Draw a tree diagram representing this scenario. (b) What s the probability that a baby was predicted to be female? (c) What s the probability that a baby is born female given that they were predicted to be female? [8 points, 2 points, 4 points] Instructor: A.E.Cary Page 5 of 8
8. An insurance policy will pay policyholders $20,000 if they suffer a major injury. It will pay $5000 if they suffer a minor injury. Assume that 3 in every 4000 policy holders will suffer a major injury and 3 in every 1000 policy holders will suffer a minor injury (a) Complete the probability model below representing the payout of a given policy. Outcome Payout Probability (b) What s the expected payout for a given policy? (c) What s the standard deviation for the payout of a given policy? [4 points, 4 points, 4 points] Instructor: A.E.Cary Page 6 of 8
9. Each year a company sends 2 officials to India and 1 official to Greece. Airline tickets vary year-toyear, but the mean price for one ticket to India is $1200 with a standard deviation of $400. The mean price for one ticket to Greece is $1800 with a standard deviation of $300. (a) Define the two random variables you will use in this problem. (b) Find the mean for the total cost of sending all three officials. (c) Find the standard deviation for the total cost of sending all three officials. [2 points, 4 points, 4 points] Instructor: A.E.Cary Page 7 of 8
10. A large computer retailer sells laptop and desktop computers. Of all the computers they sell, 60% are laptops and 40% are desktops. (a) From a sample of 8 customers buying computers, what s the probability that exactly 5 buy laptop computers? (b) Verify that you can use a Normal approximation model for a sample of 500 computers purchased. Then write down this Normal model, where the random variable is the number of laptops purchased. (In other words, specify µ and σ). (c) Out of a sample of 500 computers purchased, what s the probability that 320 or more computers are laptops? [8 points, 2 points, 6 points] Instructor: A.E.Cary Page 8 of 8