Review Questions Math 150 Exam 2 Chapter 4, 5 and 6

Transcription

1 Review Questions Math 150 Exam 2 Chapter 4, 5 and 6 Problem 1 A PC World survey of 4000 personal computers owners showed that 992 of them broke down during the first two years. In choosing among several computer suppliers, a purchasing agent wants to know the probability of a personal computer breaking down during the first two years. Use the survey results to estimate that probability. a) If a personal computer is randomly selected, what is the probability that it will break down during the first two years? b) If two personal computers are randomly selected, what is the probability that they will both break down during the first two years? Problem 2 If you make random guesses for four multiple-choice test questions (each with five possible answers), what is the probability of getting at least one correct? If a non-demanding instructor says that passing the test occurs if there is at least one correct answer, can you reasonably expect to pass by guessing? Problem 3 The following table summarizes results from 985 pedestrian deaths that were caused by accidents. Pedestrian Intoxicated Pedestrian was NOT intoxicated Driver was intoxicated Driver was NOT intoxicated a) If one of the pedestrian deaths is randomly selected, find the probability that the pedestrian was intoxicated or the driver was intoxicated. b) If one of the pedestrian deaths is randomly selected, find the probability that the pedestrian was not intoxicated or the driver was not intoxicated. c) If one of the pedestrian deaths is randomly selected, find the probability that the pedestrian was intoxicated or the driver was not intoxicated. d) If one of the pedestrian deaths is randomly selected, find the probability that the driver was intoxicated or the pedestrian was not intoxicated. e) If two DIFFERENT pedestrian deaths are randomly selected (WITH REPLACEMENT), find the probability that they both involved intoxicated drivers. f) If two DIFFERENT pedestrian deaths are randomly selected (WITHOUT REPLACEMENT), find the probability that they both involved intoxicated drivers g) Compare your results from part e) and f). Are they different or are the same or are they close?

2 h) If two DIFFERENT pedestrian deaths are randomly selected, find the probability that they both involve intoxicated pedestrians. i) If we randomly select a pedestrian death, what is the probability that the pedestrian was intoxicated, given that the driver was intoxicated? j) If we randomly select a pedestrian death, what is the probability that the driver was intoxicated, given that the pedestrian was intoxicated Problem 4 With one method of sampling, a sample of items is randomly selected without replacement, and the entire batch is rejected if there is at least one defect. The Medtyme Pharmaceutical Company has just manufactured 2500 aspirin tablets, and 2% are defective because they contain too much or too little aspirin. If 4 of the tablets are selected and tested, what is the probability that the entire batch will be rejected? Problem 5 A typical combination lock is opened with the correct sequence of three numbers between 0 and 29 inclusive. (A number can be used more than once.) What is the probability of guessing those three numbers and opening the lock with the first try? Problem 6 One company s ID cards consist of 5 letters followed by 2 digits. How many cards can be made if repetitions are allowed? If repetitions are not allowed? Problem 7 a) Construct a probability distribution for rolling a single die. b) Find the mean of the probability distribution you created above. c) Find the variance and standard deviation. d) Graph the probability distribution you created above. Problem 8 In how many ways can 8 people be selected from 10 volunteers for a drug study? Problem 9 A department has 30 members and a committee is needed to carry out a task. The committee is to be composed of two co-chairpersons and three members. How many different possible committees are there?

3 Problem 10 With one method of a procedure called acceptance sampling, a sample of items is randomly selected and the entire batch is accepted if every item in the sample is ok. The Niko Electronic Company has just manufactured 5000 CDs and 3% are defective. a) If 3 of these CDs are randomly selected for testing and we treat each trial as independent trials, what is the probability that the entire batch will be accepted? b) If 3 of these CDs are randomly selected for testing and we treat each trial as dependent, what is the probability that the entire batch will be accepted? c) Looking at your results on part a) and b) do you think it makes a difference to treat each trial independent or dependent? Explain why. Problem 11 According to American Airlines, its flight 215 from Orlando to Los Angeles is on time 90% of the time. Suppose 15 flights are randomly selected. a) Explain why this is a binomial experiment b) Find the probability that exactly 14 flights are on time c) Find the probability that at least 14 flights are on time. Problem 12 What is the ideal number of children to have in a family? The following data represents the ideal number of children for a random sample of 900 adults. X (Number of Frequency Children) a) Is this a probability distribution? Why or why not? b) Construct a probability distribution table for the information given c) What is the mean? Write a sentence explaining what this number means in terms of the problem. d) What is the probability that a randomly selected adult wants to have at least 3 children in a family?

4 Problem 12 An engineer wanted to determine how the weight of a car affects gas mileage. The following data represent the weights of various domestic cars and their gas mileages in the city for the 2008 model year. Car Weight (in pounds) Miles per Gallon Buick Lucerne Cadillac De Ville Chevrolet Malibu Chrysler Sebring Sedan Dodge Neon Dodge Charger Ford Focus Lincoln LS Mercury Sable Pontiac G Saturn Ion a) Construct a scatter plot for the data. Please make all appropriate labels!! b) Using your calculator, find the correlation coefficient ( r ). Do you think there s a relationship between the weight of car and its miles per gallon in the city? If so, explain.. c) Using your calculator, find the equation of the linear regression line. d) Using the regression line you found above, find the mileage per gallon of a car weighing 2750 lbs. Please show your work Problem 13 Outdoor temperature influences natural gas consumption for the purpose of heating a house. The usual measure of the need for heating is heating degree days. The number of heating degree days for a particular day is the number of degrees the average temperature for that day is below 65 F, where the average temperature for a day is the mean of the high and low temperatures for that day. An average temperature of 20 F, for example, corresponds to 45 heating degree days. A homeowner interested in switching to solar heating panels collects the following data on her natural gas use for the months October through June, where x is heating degree days per day for the month and y is gas consumption per day in hundreds of cubic feet. Month Oct Nov Dec Jan Feb Mar Apr May June x y a) Draw a scattler plot. Please draw the vertical and horizontal and LABEL, LABEL, LABEL!!! b) Using calculator, calculate the correlation coefficient and interpret what it means. c) Using your calculator, find the equation of the linear regression line. d) Find the heating per day, if the gas consumption is 10.

5 Problem 14 Suppose a compact disk (CD) you just purchased has 13 tracks. After listening to the CD, you decide that you like 5 of the songs. With the random feature on your CD player, each of the 13 songs is played once in random order. Find the probability that among the first two songs played a) You like both of them? Would this be unusual? Explain why b) You like one of the songs. Problem 15 Show your work. If you re using your CALC, tell me what you re doing. In the following table, the random variable X represents the number of activities a parent of a 3 rd grade student is involved in. X P ( X ) e) Is this a probability distribution? Explain why. f) Find μ, and interpret the meaning of the answer you found. g) What is the standard deviation? h) What is the probability that a randomly selected student has a parent involved in three activities? i) What is the probability that a randomly selected student has a parent involved in at least 2 activities?