Review “Probability Distributions” Name __________________________________ I) Identify as much information as possible. This may include any of the following: n, p, q, μ, σ, or x. II) Decide which method to use to solve each problem: BPD – binomial distribution (with formula) ND – normal distribution (includes inverse) NA – binomial distribution using the normal approximation III) Show all work to solve problems. Express answers as rational numbers when possible; otherwise round percents to nearest hundredth. BPD: Write formula with given values; indicate if you are using the complement. ND: Find z and the corresponding percent if possible. Draw, label, and shade the bell-curve. NA: show that NA can be used; “correction for continuity” for x (add and/or subtract 0.5); follow steps for ND Binomial Probability Distribution 1. A quarter is flipped five times. Find the probability of getting: a) exactly three tails b) no more than four heads 2. 5% of all items checked by scanners at the grocery store are given the wrong price. What is the probability that more than 2 items out of 16 are wrongly priced? Normal Distribution 3. It takes a certain pain reliever 30 minutes to begin reducing symptoms, with a standard deviation of 4 minutes. Find the probability that it will take: a) between 34 and 35 minutes to begin working b) more than 35 minutes to begin working c) less than 25 minutes to begin working d) between 35 and 40 minutes to begin working 4. The average height of a certain group is 53 inches, with a standard deviation of 4 minutes. Find the probability that the height will be: a) greater than 59 inches b) less than 45 inches c) between 50 and 55 inches d) between 58 and 62 inches 5. The average test score for stress tolerance for security officers is 62. If 15% scored above 70, find the standard deviation. Inverse Normal Distribution 6. (Solve using the bell curve) The average thickness of a book on a library shelf is 8.3 centimeters. The standard deviation is 0.6 centimeters. If 20% of the books are undersized, find the maximum thickness of the undersized books. 7. Membership in an elite organization requires a test score in the upper 30% range. If the mean is 115 and the standard deviation is 12, find the lowest acceptable score that would enable a candidate to apply for membership. Normal Approximation to the Binomial Distribution 8. The probability of winning on a slot machine is 8%. If a person plays the machine 300 times, find the probability of winning at most 20 times. 9. If 10% of the people in a certain factory are members of a union, find the probability that, in a sample of 2000, fewer than 180 people are union members. 10. The percentage of U.S. households which have online connections is 44.9%. In a random sample of 420 households, find the probability that at least 200 have online connections. Mixed Review 11. The average number of gallons of lemonade consumed by a team during a game is 20, with a standard deviation of 3 gallons. Find the probability of the team drinking: a) between 20 and 25 gallons b) less than 19 gallons c) more than 21 gallons d) between 26 and 28 gallons 12. 70% of students oppose a new parking lot that will require the destruction of several dozen large spruce trees. A random sample of 20 students was asked about the proposed parking lot. Find the probability that; a) at least 15 oppose the new parking lot b) no more than 10 oppose the new parking lot 13. The speed limit on a certain interstate is 65 mph. On a clear day, the average speed was measured at 63 mph with standard deviation of 8 mph. If the Highway Patrol decides to ticket only those exceeding 72 mph, what percent of motorists might get a ticket? 14. In a large university, 30% of incoming freshmen enroll in a personal finance course. Of 800 randomly selected freshmen, find the probability that at least 260 enroll in the course. 15. The average age of graduate school students is 26.5 years. If 30% of the students are older than 28, find the standard deviation. 16. 12% of American drivers talk on the cell phone while driving. If 300 drivers are selected at random, find the probability that exactly 40 talk on the cell phone while driving. 17. The average weight of an airline passenger’s suitcase is 45 pounds. The standard deviation is 2 pounds. If 15% of the suitcases are overweight, find the maximum weight allowed by the airline. 18. On a daily bus route, the average number of passengers is 48. The standard deviation is 3. Find the probability that the bus will have; a) between 36 and 40 passengers b) fewer than 42 passengers c) more than 48 passengers d) between 43 and 47 passengers 19. An educational study to be conducted requires a test score in the middle 40% range. If the mean is 100 and the standard deviation is 15, find the highest and lowest acceptable test scores that would enable a candidate to participate in the study. 20. Fifty-three percent of U.S. households have a personal computer. In a random sample of 250 households, find the probability that more than 120 have a personal computer. 21. The average number of years it takes a person to complete a graduate degree is 3. The standard deviation is 4 months. Find the probability that it will take: a) more than 4 years to complete the program b) less than 3 years to complete the program c) between 3.8 and 4.5 years to complete the program d) between 2.5 and 3.1 years to complete the program 22. Of the total population of the U.S., 20% live in the northeast. If 200 residents are selected at random, find the probability that at least 50 live in the northeast. 23. Richard has just been given a 10-question multiple choice quiz in history class. Each question has three answers, of which only one is correct. If Richard guesses on all the questions, find the probability that he will answer: a) all of the questions correctly b) none of the questions correctly c) only six of the questions correctly 24. Of the total population of older Americans, 18% live in Florida. For a randomly selected sample of 200 older Americans, find the probability that more than 40 live in Florida. 25. The average price of a new home is $188,000. Find the maximum and minimum house prices a contractor will build to include the middle 70% of the market. The standard deviation is $1500.