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a) The average age of the students in a statistics class is 21 years. ... What is the probability that the next person that answers to the survey says that ...
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d) temperatures of 22 selected refrigerators e) number of milligrams of tar in 28 cigarettes f) number of pages in your statistics book g) marriage status of the faculty at the local community college h) list of 1247 social security numbers i) the ratings of a movie ranging from “poor” to “good” to “excellent” j) the final grades (A,B,C,D, and F) for students in a chemistry class k) the annual salaries for all teachers in Utah l) list of zip codes for Chicago m) the nationalities listed in a recent survey n) the amount of fat (in grams) in 44 cookies o) the data listed on the horizontal axis in the graph Five Top-Selling Vehicles 0 10 20 30 40 50 60 70 Vehicles sold (in thousands) Series1 62 41 28 26 31 Ford F-Series Chevrolet Silverado Dodge Ram Ford Explorer Toyota Camry
2.1 Frequency Distributions and Their Graphs Example 1: The following data set lists the midterm scores received by 50 students in a chemistry class: 45 85 92 99 37 68 67 78 81 25 97 100 82 49 54 78 89 71 94 87 21 77 81 83 98 97 74 81 39 77 99 85 85 64 92 83 100 74 68 72 65 84 89 72 61 49 56 97 92 82 Construct a frequency distribution, frequency histogram, relative frequency histogram, frequency polygon, and cumulative frequency graph (ogive) using 6 classes. Example 2: The heights (in inches) of 30 adult males are listed below. 70 72 71 70 69 73 69 68 70 71 67 71 70 74 69 68 71 71 71 72 69 71 68 67 73 74 70 71 69 68 Construct a frequency distribution, frequency histogram, relative frequency histogram, frequency polygon, and cumulative frequency graph (ogive) using 5 classes.
Example 5: You have been in the walking/jogging exercise program for 20 weeks, and for each week you have recorded the distance (in miles) you covered in 30 minutes. Week 1 2 3 4 5 6 7 8 9 10 Distance 1.5 1.4 1.7 1.6 1.9 2.0 1.8 2.0 1.9 2. Week 11 12 13 14 15 16 17 18 19 20 Distance 2.1 2.1 2.3 2.3 2.2 2.4 2.5 2.6 2.4 2.
2.3 Measures of Central Tendency Example 1: The top 14 speeds, in mph, for Pro-Stock drag racing over the past two decades are: 181.1 202.2 190.1 201.4 191.3 201.4 192. 201.2 193.2 201.2 194.5 199.2 196.0 196. Example 2: The scores of the top ten finishers in a recent golf tournament: 71 67 67 72 76 72 73 68 72 72 Example 3: The ages of 21 cars randomly selected in a student parking lot: 12 6 4 9 11 1 7 8 9 8 9 13 5 15 7 6 8 8 2 1 5 Example 4: You are taking a class in which your grade is determined from: Quizzes: 15% total Exams (3): 15% each Homework: 10% Final: 30% Your scores are: average quiz mean = 85, exams =78, 81, 92, homework mean = 85 and your final = 89. a) If the minimum average for B+ is 87, did you get B+ at the end of the semester? b) What if the quiz mean was not given, but the quiz scores are given as 10, 12, 8, 2, 9, 7 (out of 12 points each), and only best 4 quizzes count towards your grade? Example 5: The average starting salary for 50 employees at a company is given: 10 with high-school diploma: $27,000 each 25 with BA/BS degree: $ 35,000 each 10 with MA/MS degree: $47,000 each 5 with Ph.D. degree: $59,500 each How would you find the starting mean salary for these employees? Would you add the 4 $ amounts and divide by 4? Explain Example 6: Approximate the mean of the grouped data: Heights of Males (inches) Frequency 63 - 65 3 66 - 68 6 69 - 71 7 72 - 74 4 75 - 77 3
Example 6: How long will it take you to graduate from college? (These are responses from a sample of students on campus.) Years f 3 10 4 48 5 25 6 10 7 6 8 1 Assuming the bell-shaped distribution (normal distribution): What percentage of students will need: a) more than 7.9 years to graduate? b) between 3.5 and 5.7 years to graduate? c) more than 1.3 years to graduate? Example 7: The mean time in a women’s 400-m dash is 57.07 s, with a standard deviation of 1.05 s. a) Apply Chebychev’s Theorem to the data using k=3. Explain the meaning of the values that you find. b) If there is a sample of 350 women, about how many would have time between 54.97 s and 59.17 s? Example 8: In a random sample, 10 students were asked to compute the distance they travel one way to school to the nearest tenth of a mile. The data is listed: 1.1 5.2 3.6 5.0 4.8 1.8 2.2 5.2 1.5 0. a) Using Chebychev’s Theorem, approximate the percentage of students travel between 0 and 6.76 miles (one way) to school. b) If there are 25,000 students on campus, approximate the number of students who travel between 0 and 6.76 miles (one way) to school. Example 9: SAT verbal scores are normally distributed with a mean of 489 and a standard deviation of 93. Use the Empirical Rule (also called 68- 95 - 99.7 Rule) to determine what percentage of the scores lie: a) between 303 and 582. b) above 675? c) If 3,500 students took the SAT verbal test, about how many received between 396 and 675 points?
Example 10: The batting averages of Sammy Sosa and Barry Bonds for 13 recent years: Sosa: € x _ = 0.279, s = 0. Bonds: € x _ = 0.312, s = 0. Which player is more consistent? Why? Example 11: Which data set has the highest a) mean , b) standard deviation i) 0 9 ii) 0 iii) 10 9 1 5 8 1 5 8 9 11 5 8 2 3 3 7 7 2 3 3 7 3 12 3 3 7 7 3 2 5 3 2 5 6 13 2 5 4 1 4 14 1 Example 12: Data entries: a b c d Mean of a, b, c, d is € x _ , and the standard deviation is s. What will happen to the mean and standard deviation if we add 5 to each data entry? What will happen to the mean and standard deviation if each data entry is 3 times larger.
3.1 Basic Concepts of Probability and Counting
3.4 Additional Topics in Probability and Counting