CH4-Assignment

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Apr 3, 2024

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Module 4 (Chapter 4) Assignment Problem 1 How many permutations of three items can be selected from a group of six? Use the letters A, B, C, D, E, and F to identify the items, and list each of the permutations of items B, D, and F. 120 permutations can be selected from a group of 6. 6 permutations can be made with the items of B, D, F. The following permutations are BFD, BDF, DBF, FBD, FDB. To find the permutations of the three items that can be selected, you can use the formula N! / (N - n)! where N is 6, the total number in the group, and n is 3, the number to be selected. Using a tree diagram, you can list the permutations of items B, D, and F. Problem 2 The National Highway Traffic Safety Administration (NHTSA) conducted a survey to learn about how drivers throughout the United States are using seat belts (Associated Press, August 25, 2003). Sample data consistent with the NHTSA survey are as follows: Region Driver Using Seat Belt? Yes No Northeast 148 52 Midwest 162 54 South 296 74 West 252 48 Total 858 228 a. For the United States, what is the probability that a driver is using a seat belt? The probability that a driver is using a seat belt in 2003 is 0.79. To find this probability, you can calculate it by dividing the total number of individuals using seat belts by the sum of the total number of people who use seat belts and those who don't. b. The seat belt usage probability for a U.S. driver a year earlier was .75. NHTSA chief Dr. Jeffrey Runge had hoped for a .78 probability in 2003. Would he have been pleased with the 2003 survey results? Yes, because the probability of a driver using a seat belt increased by 0.04 percent (from 0.75 to 0.79). The probability is 0.01 better than what Dr. Runge had hoped for. c. What is the probability of seat belt usage by region of the country? What region has the highest seat belt usage? Northeast probability is .74. Midwest probability is .75. South probability is .80. West probability is .84. The West region has the highest seat belt usage. To find the probability of seat belt usage for each region, you can do so by taking the total count from the "yes" column of the specific region and dividing it by the total count of responses for that region, considering only those who wear seat belts. d. What proportion of the drivers in the sample came from each region of the country? What region had

the most drivers selected? What region had the second most drivers selected? Northeast proportion: 200 total drivers, 0.18 of drivers in all the regions. Midwest proportion: 216 total drivers, .20 of the drivers in all the regions. South proportion: 370 total drivers, .34 of the drivers in all the regions. West proportion: 300 total drivers, .28 of the drivers in all the regions. The region with the most selected drivers was the South, followed by the West region with the second-highest number of selected drivers. To calculate the total number of drivers in each region, you need to sum both the drivers who wear seat belts and those who don't. To find the proportion for each region, divide the total number of both drivers who wear and don't wear seat belts by the overall total for each of the regions. e. Assuming the total number of drivers in each region is the same, do you see any reason why the probability estimate in part (a) might be too high? Explain. Assuming the total number of drivers in each region is the same, the reason why the probability estimate might be too high is that the number of drivers may not be truthful in their responses. There could be errors in collecting the responses, or the survey takers might have favored one region over another, which is why one region appears to have more drivers. Problem 3 The U.S. adult population by age is as follows (The World Almananc, 2009). The data are in millions of people. Age Number 18 to 24 29.8 25 to 34 40.00 35 to 44 43.4 45 to 54 43.9 55 to 64 32.7 65 and over 37.8 Assume that a person will be randomly chosen from this population. a. What is the probability the person is 18 to 24 years old? The probability that a person is between 18 to 24 years old is 0.13. To calculate this probability, you need to divide the number of people whose age falls within the 18 to 24 range by the overall total of all age groups. b. What is the probability the person is 18 to 34 years old? The probability that a person is between the ages of 18 to 34 is 0.31. To calculate this probability, you can add the sum of both age groups (18 to 24 and 25 to 34) and then divide it by the overall total of all the age groups. c. What is the probability the person is 45 or older? The probability that a person is 45 or older is 0.502. To calculate this probability, you can find the sum of the three age groups (45 to 54, 55 to 65, and 65 and over) and then divide it by the overall total of all the age groups. .

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