Exam 4 5 MAT108 Online Summer 2022

MAT108 Online, Summer 22 Name:______Taylor Henderson_____ Exam 4 & 5: Probability & Statistics Directions: There are 36 questions worth 5 points each, and two questions worth 10 points each. Proper work must be shown to receive any credit. 1. In a large lecture hall there are 325 students of which 160 are male and 165 are female. If one student is selected at random, determine the empirical probability the individual selected is male. 160/325 = .4923 = 49.23% 1._____49.23%_______ 2. Mr. Peters’ grade distribution over the past 3 years of a course in college algebra is shown in the chart below. If Sue plans to take college algebra with Mr. Peters, determine the empirical probability that she receives a B. Write your answer as a simplified fraction. 82+30+24+14+10=160 30/160=.1875 =18.75% 2. 18.75%_________ Grade Number A 82 B 30 C 24 D 14 F 10 3. A card is selected from a standard deck. Find the probability of selecting: a) a king. 4/52= .0769 = 7.69% 3a.____7.69%____ b) a number greater than 10. 3b._____30.77%_____ jack , queen, king, ace x 4 suits= 16 16/52 =.30769 = 30.77% 4. The table shows the type and manufacturer or vehicles at a car dealership. If one person selects a vehicle at random, determine the probability that the person selects an SUV. 49/140 = .35 = 35% 4.____35%________

R R G G R B Domestic Foreign Total Car 60 31 91 SUV 32 17 49 Total 92 48 140 5. If the probability that an event occurs is 2 7 , then what is the probability that the event does not occur? 5._____71.43%____ 5/7 = .7143 = 71.43% 6. a) The sum of the probabilities of all possible outcomes of an experiment is _1__ b) Every probability is a number between ____0__ and ___1___, inclusive. 7. Determine the odds against rolling a 5 on one roll of a die. 7.______16.67%____ 1/6 = .1667 = 16.67% 8. A box contains 6 balls: 3 red, 2 green, and 1 blue. One ball is selected at random. Determine the odds in favor of selecting a green ball. 8._____33.33%______ 2/6 = .3333 = 33.33% 9. The odds against Robin being admitted to the college of her choice are 9:2. Determine the probability that Robin is admitted. 7/9 = .7778 = 77.78% 9.____77.78%_____

14. A dinner special consists of a soup, an entrée, and a dessert. The choices are listed. Construct a tree diagram and list the sample space. Soup Entrée Dessert Vegetable Pork Chops Apple Pie French Onion Ravioli Ice Cream Chocolate Cake 15. A coin is tossed and a die is rolled. Assume each event is equally likely to occur. Determine the probability of getting V PC A V PC I V PC C V R A V R I V R C FO PC A FO PC I FO PC C FO R A FO R I FO R C SAMPLE SPACE IS 12

a) a head on the coin and an odd number on the die. 15a.____25%________ 3/12 = .25 = 25% b) a tail and a 5. 1/12 = .08 = 8% 15b._____8%_______ 16. One card is selected from a standard deck of playing cards. Let Q = a queen is selected. Let J = a jack is selected. a) Are these events mutually exclusive?__YES_______ b) Explain. They are mutually exclusive because it is impossible for both to be picked simultaneously when only one card is being selected. 17. A die is rolled one time. Determine the probability of rolling an even number or a number less than 4. 17.___83% ________ Even numbers: 2,4,6 Less than4: 3,2,1 Both categories include 2. For a total of 5/6 chance = .83 = 83% 18. One card is selected from a standard deck of playing cards. Determine the probability of selecting a 10 or an ace. 18.______15.4%_____ 4 tens + 4 aces = 8 cards total 8/25 = .1538 = 15.4% 19. A box contains 3 red, 2 green, and 1 blue ball. Two balls are selected at random, with replacement , determine the probability that both are blue.

22. A sample that is a small replica of the entire population is called a(n) ___random______ sample. 23. Circle the sampling technique used. Every 100 th two-liter bottle of Coca-Cola coming off an assembly line is checked to see how many ounces of soda it contains. a. random b. systematic c. cluster d. stratified e. convenience 24. Read the statement and explain what possible misuse or misinterpretation may exist. More women than men are involved in automobile accidents. Therefore, women are worse drivers. The was misinterpreted for several reasons. The number of those in an accident compared to the total number of drivers is not taken into account. It does not address the type of accidents and list whose fault the accidents were, just that they were in an accident. 25. Use the frequency polygon, concerning response time for selected emergency calls, to answer the following questions: a) The number of calls that were responded to in 10 minutes is ___4__. b) The total number of calls in the survey is _40__. 26. Use the following data, which represent the ages of the 44 U.S. presidents at their first inauguration (as of 2011), to construct a frequency distribution with a first class of 42-47.

57 57 49 52 50 42 54 55 64 61 61 64 56 47 51 51 56 46 57 54 50 46 55 56 60 61 54 57 68 48 54 55 55 62 52 47 58 51 65 49 54 51 43 69 27. Construct a frequency polygon for the following frequency distribution. AGE FREQUENCY 42-47: 6 48-53: 11 54-59: 17 60-65: 8 66-71: 2 Starting Salaries of Social Workers Salaries (thousands of dollars) Number of Social Workers 27 2 28 1 29 4 30 6 31 3

30. The prices per gallon of the 21 top-rated interior paints follows: $18 19 19 19 20 20 21 21 22 22 23 23 25 27 30 33 35 35 35 58 61 30a. Q 2 =___23___ 30b. Q 1 =__20_____ 30c. Q 3 =___34____ 31. Determine the range and standard deviation of this set of data. Round to the nearest hundredth. 4 8 9 11 13 15 31. range = ______11______ standard deviation = 3.9 32. Sketch a skewed left distribution. Use the line below to help. ___________________________ 36+4+1+1+9+25/6-1 = 15.2 15.2 = 3.90 X X-MEAN (X-MEAN) squared 4 4-10= -6 36 8 8-10= -2 4 9 9-10= -1 1 11 11-10=1 1 13 13-10=3 9 15 15-10 =5 25

33. Sketch and label the normal curve with a mean of 100 and a standard deviation of 15. Label the mean and the three standard deviations above and below the mean. 34. According to the empirical rule, in a normal distribution, approximately ____68___% of the data lie within plus or minus 1 standard deviations of the mean. If there are 500 pieces of data then approximately ___340__ pieces of data lie with plus or minus 1 standard deviations of the mean. .68 x 500 = 340 35. Intelligence quotients (IQ scores) are normally distributed with a mean of 100 and a standard deviation of 15. Find the z-score for each of the following IQ scores. Round to the nearest hundredth. a) 142 15a.______2.8______ 142-100 = 42 42/ 15 = 2.8 b) 73 15b.____-1.8_____ 73-100= -27 -27 / 15 = -1.8

37. Use the internet to find an example/article where someone uses odds or a probability. This should be easy to find. Write a short paragraph explaining what you found and what it means. Your audience is someone who walks around saying “I hate math. I can’t do math.” You can also copy/paste/insert the example you find here as well so I know what you are talking about. (10 points) The Insurance Information Institute wrote an article called Facts + Statistics: Motorcycle Crashes. The information outlined in this article is from 2020. The source of their statistics comes from the U.S. Department of Transportation, National Highway Traffic Safety Administration. In 2020 out of every 100,000 registered vehicles in the U.S. there were 67.08 motorcycle fatalities, 6.90 light truck fatalities and 10.79 passenger car fatalities. This tells us that you are over 6 times more likely to be killed on a motorcycle than you are in a passenger car. Also you are 9.72 times more likely to die on a motor cycle than in a truck. Additionally, the article outlines that your highest chance of getting into a fatal accident on a motorcycle is 3pm-6pm on a weekday and 6pm-9pm on a weekend. 38. Use the internet to find an example/article where someone misuses statistics. This can be to try to sell a product, push an agenda, or otherwise influence opinion. Write a short paragraph explaining how statistic(s) is being used to manipulate. You can also copy/paste/insert the misuse you find here as well so I know what you are talking about. (10 points) In 2007 Colgate Toothpaste ran an advertisement claiming that “More than 80% of dentists recommended Colgate.” And “Colgate is used and recommended by most dentists.” This information was misleading because it implied that the dentist recommended Colgate over any other brand. In reality, in the survey the dentists and hygienists were asked for multiple product recommendations, not just one product. Therefore, it is noted that Colgate conveniently left out the information that other products were recommended equally as often. https://marketinglaw.osborneclarke.com/retailing/colgates-80-of-dentists-recommend-claim- under-fire/