Probability and Statistics Test Review SheetMath 1361. The mayor of Jersey City would like to build a new stadium. Suppose you have been hired by him to find out if there is public support among college students in Jersey City for a new stadium. You decide to sample 100 college students in Jersey City. Suppose there are about 20,000 students in Jersey City.a. Clearly define your population.b. Explain in detail how you would obtain your sample by a systematic method.c. Explain in detail how you would obtain your sample by a simple random method.d. Explain in detail how you would obtain your sample by a stratified method.e. Explain in detail how you would obtain your sample by a cluster method.f. What is wrong with using a sample of fans selected as they leave a stadium just after a game? 2. How many different languages are spoken by Brookdale students? To find the answer to this question a random sample of 50 students who belong to the International Center was contacted.a. What is the population that is being discussed?b. Is this the actual population that is being used to produce the sample? Explain.c. What is the sample?d. Does this sample represent the population well?e. Can we generalize these results to all college students in the U.S.? Explain. 3. The ages of 10 U.S. Presidents (when they were elected) randomly chosen from this century are as follows: 42 56 51 51 62 55 61 69 51 55 a. Find the mean, median and mode for this set of data.b. Which of these three averages best represents the majority of the data? Explain why. (Hint: are there any extreme scores?)c. Make a stem-and-leaf diagram for this data.d. What does the stem-and-leaf diagram tell you about the presidents’ ages? 4. The following data represents the average number of students in public high schools for states along the East Coast and in New England. 668 815 2,225 981 483 960 745 652 790 818 789 535 933 821 911 857 a. Find the mean, median and mode for this set of data.b. If you could only present one of these as the "average", which would you choose and why?c. Organize this data into five or six groups.d. Make a bar graph for this data.e. Comment on your data, using the graph as a guide.f. Find the four quartiles and explain what each one tells you about the data. 5. Name one advantage stem-leaf diagrams have over bar graphs, and one disadvantage(Hint: imagine trying to make a stem-leaf diagrams of the data in the previous problem).6. Jennifer is interested in determining the best route to drive to school. During one week she drove to school on the turnpike and during the second week she drove on the parkway. The number of minutes spent driving to school was: Turnpike: 15 26 30 39 45 Parkway: 29 30 31 32 33a. Compute the mean for each set of data.b. Intuitively, which set of data is more spread out from the mean?c. Compute the standard deviation for each set of data.d. Do your answers for (b) and (c) agree? EXPLAIN.e. Based on the standard deviation, which way would you rather drive to school? Explain.7. What can be said about a set of data with standard deviation of zero?8. a. If you take a test with 100 questions and receive a score in the 50th percentile, does that mean you got 50 right out of the 100 questions?b. Ianna just took a test in which she was in the 99th percentile, yet she did not pass the test. How could this happen?9. Considering how common international travel has become, you are asked to investigate the number of resident U.S. citizens in a country, x and the number of U.S. tourists in the same country, y. You use the Statistical Abstract of the United States, 1994and randomly choose 12 countries for your study. The information you collected is recorded below: Country x = number of U.S. citizens who are residents (in thousands) y = number of U.S. tourists (in thousands)Argentina 13 11Canada 296 495Dominican Republic 97 36France 59 89Greece 32 60Ireland 46 86Italy 104 105Israel 112 61Panama 36 2Saudi Arabia 40 6Spain 79 155United Kingdom 255 377a. Draw a dot plot for this data. Does it look like there may be a positive or negativecorrelation? Explain.b. Is the correlation coefficient, r = 0.94454 significant at the 0.05 level? c. What does this correlation mean? Explain.10. a. Would the correlation between the age of a used car and its price be positive or negative? Explain. (Antique cars are not included.)b. In the above example, what would happen to the correlation if we only looked at antique cars?c. Would the number of days absent from class and the grade received in the class have a positive, negative or zero correlation? Explain.d. Some researchers have found that there is a positive correlation between coffee drinking and the risk of heart disease. Does this mean that coffee drinking causes heart disease? What third factor could be causing both factors to increase? 11. The following two histograms show the results of surveys of the dining habits in two towns:a. How many people were surveyed in Barnsville?b. How many people in the Barnsville survey spent between $0 and $9 eatingout?c. If a person in Barnsville is picked out at random, what’s the probability they will have spent between $0 and $9 on eating out?d. Find the mode (or modal class) for each graph.e. Explain what the two graphs tell you about how the two towns are different.12. Find at least three things wrong with the graph below, and how each of these things will affect the way we perceive the data.13. Explain what is wrong with the following statement: Most accidents happen in the home, so it is best not to spend any time at home.14. a. How many possible 4-digit passwords can I have if the first digit cannot be a zero, and the next digits can be any number from 0 to 9?b How many possible 4-digit passwords can I have if the first digit can be any number from 0 to 9 and no digits can be repeated?15. If I roll a 12-sided die (with numbers 1 to 12 on it):a. What’s the probability I’ll get a number greater than 7?b. What’s the probability I’ll get a number greater than 12?c. What’s the probability I’ll get a number that is 12 or less?d. What’s the