MAT 142 Practice Problems (with answers) Module 4, Statistics 1. Given this data, find the mean, standard deviation and the percentage of data within one standard deviation of the mean: 16, 15, 17, 20, 19, 20, 18, 13, 15, 16, 17, 14, 15, 18, 20, 23 2. Using the same data as in problem 1, state the five number summary. 3. Below is a box-whisker plot. State the five number summary: Min___, Q1___, Med___, Q3___, Max___ 4. Below is a set of data representing the speeds of motorists on the Loop-202 over a five minute period. 71 73 74 67 52 56 80 76 81 75 74 70 69 65 65 64 67 59 58 58 67 71 72 58 58 72 73 67 73 54 55 57 80 82 85 78 76 74 72 74 72 74 74 75 67 66 67 74 74 76 78 79 70 68 63 65 a) Form this data into a frequency chart. Use classes 51-60, etc. b) Form this data into a stem-leaf diagram? c) What is the median of this data based on the stem-leaf diagram? d) Using your calculator, enter all this data, one by one. State the mean, standard deviation and the 5-number summary. 5. On a standard normal curve, what is the area to the left of z = 2.05? 6. On a standard normal curve, what is the area to the left of z = -1.54? 7. On a standard normal curve, what is the area to the right of z = 0.67? 8. On a standard normal curve, what is the area to the right of z = -1? 9. On a standard normal curve, what z-score corresponds to the 64th percentile? 10. On a standard normal curve, what z-score corresponds to the 35th percentile? 11. On a standard normal curve, what z-score corresponds to the top 15 percent? 12. On a standard normal curve, what z-score corresponds to the top 3 percent? 13. Weights of bags of chips have a mean of 30 g, with a standard deviation of 4 g, distributed normally. What percentage of bags will weigh between 22 g and 28 g? 14. In question 13, what percentage of bags will weight above 32.5 g?15. In question 13, any bag that at or below the 20th percentile is thrown out. What weight (in grams) would get a bag thrown out? 16. SAT scores are normally distributed with a mean of 1500 and a standard deviation of 280. What percentage of students scored between 1200 and 1790? 17. In question 16, what percentage scored at or below 2000? 18. In question 16, a student gets a scholarship if they fall in the top 5%. What score gets the student a scholarship? 19. In question 16, any student who scores in the 70th percentile gets a candy bar. What score gets the student a candy bar? 20. Dave has test scores of 79, 91, 80 and 83. He needs to maintain an 85 average. He has one more test. What score does he need to maintain his 85 average? 21. One lovely summer month, the daily highs in Phoenix were: 109, 109, 107, 108, 109, 110, 112, 110, 112, 114, 112, 113, 110, 110, 109, 107, 109, 108, 109, 109, 110, 110, 109, 103, 104, 104, 110, 109, 111, 108, 105. a) Form this data into a frequency chart. Use the individual scores, no classes. b) What is the mean, standard deviation, five-number summary? c) What is the mode? 22. Star basketball player Scott (the Conquistador of Slams) Sgurnet averaged 30 points over a nine-game stretch. If he scores 40 in the 10th game, what was his average points per game over the 10 games? ANSWERS 1. Mean = 17.25, Standard deviation Sx = 2.671. Ten of seventeen data points were within one st.dev of the mean, so 10/17 = 58.8%. The interval was (14.579, 19.921). 2. Min = 13, Q1 = 15, Med = 17, Q3 = 19.5, Max = 23 3. Min: 22, Q1: 26, Med: 30, Q3: 39, Max: 41 4. A) 51-60: 10; 61-70: 16; 71-80: 27; 81-90: 3 B) 8|00125 7|001122223334444444455666889 6|34555677777789 5|2456788889 C) Med=71.5 D) Mean = 69.535, St.Dev = 7.769, Min = 52, Q1 = 65, Med = 71.5, Q3 = 74, Max = 85 5. normalcdf (-5,2.05,0,1) = 0.9798 (Use -5 as a lower bound if one is not given) 6. normalcdf (-5,-1.54,0,1) = 0.0618 7. normalcdf (0.67,5,0,1) = 0.2514 (Use 5 as an upper bound if one is not given) 8. normalcdf (-1,5,0,1) = 0.8413 9. z = InvNorm (0.64,0,1) = 0.358510. z = InvNorm (0.35,0,1) = -0.3853 11. z = InvNorm (0.85,0,1) = 1.0364 (Top 15% is the same as the 85th percentile) 12. z = InvNorm (0.97,0,1) = 1.8808 (Top 3% is the same as the 97th percentile) 13. normalcdf(22,28,30,4) = 0.2858 or 28.58% 14. normalcdf (32,100,30,4) = 0.3085 or 30.85% (Use 100 as a top bound as it’s far away) 15. InvNorm (0.2,30,4) = 26.6335 grams. 16. normalcdf (1200,1790,1500,280) = 0.7078, or 70.78% 17. normalcdf (0,2000,1500,280) = 0.9629 or 96.29% 18. InvNorm (0.95,1500,280) = 1960.55 19. InvNorm (0.7,1500,280) = 1646.83 = candy bar, mmmm. 20. Let x be his test score. We want the average of the 5 tests to be 85: = 85. Cross multiply, and sum the scores in the top row: 333 + = 425. Subtract: = 425 − 333 = 92. He needs at least a 92. 21. A) temp | freq 103 | 1 104 | 2 105 | 1 106 | 0 107 | 2 108 | 3 109 | 9 110 | 7 111 | 1 112 | 3 113 | 1 114 | 1 b) Use L2 for frequencies. Type 1-Var Stats L1, L2. Mean = 109, Sx = 2.5299, Min = 103, Q1 = 108, Med = 109, Q3 = 110, Max = 114. c) Mode = most often = 109. 22. = 31 Points per game. (No relation to your
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