Chapter 2 1. Describe the distribution. survival times of persons diagnosed with terminal lymphoma A) approximately normal B) skewed left C) skewed right D) roughly uniform Ans: C Difficulty: low 2. Without doing any computation, estimate the mean and standard deviation of beagle weights. A) mean = 12; standard deviation = 2 C) mean = 8; standard deviation = 12 B) mean = 12; standard deviation = 4 D) mean = 8; standard deviation = 4 Ans: A Difficulty: low 3. This diagram shows a uniform distribution on [3, 21], the interval from 3 through 21. 3 21 What values enclose the middle 50% of the distribution? A) 6.75 to 11.25 B) 4.5 to 13.5 C) 3 to 9 D) 3 to 21 Ans: B Difficulty: low 4. The average of a set of seven quiz scores is 70. Six of the values are 91, 66, 74, 51, 70, and 74. What is the 7th value? A) 81 B) 61 C) 71 D) 64 Page 1
5. The sum of a set of quiz scores is 750 and the mean is 75. How many values are there? A) 11 B) 12 C) 15 D) 10 Page 2
6. Match the histogram to its boxplot. A) B) C) D) Ans: B Difficulty: low Page 3
7. A web site hosting service counted the number of hits in one day for a set of eleven web sites. These data are shown below. 151, 88, 74, 69, 69, 66, 62, 59, 54, 43, 2 Draw a boxplot, showing any outliers, of the number of web site hits for all eleven sites. Ans: Difficulty: medium 8. The mean of each of these sets of values is 45, and the range is 60. Which set has the largest standard deviation? No computing should be necessary. I. 15, 30, 45, 60, 75 II. 15, 15, 45, 75, 75 III. 15, 45, 45, 45, 75 IV. 15, 29, 45, 31, 75 A) I. B) II. C) III. D) IV. Ans: B Difficulty: medium 9. Two of these sets of values have a standard deviation of about 8. Which two? No computing should be necessary. I. 9, 17, 25, 33, 41 II. 15, 19, 23, 27, 31 III. 20, 20, 20, 20, 20, 20, 20, 20, 20 IV. 20, 22, 24, 26, 28, 30, 32, 34, 36 A) II. and IV. B) I and II. C) III. and IV. D) I. and III. Ans: A Difficulty: medium 10. The standard deviation of the first set of values listed here is about 35. What is the standard deviation of the other set? Explain. 12, 32, 48, 74, 97, 107, 117 20, 40, 56, 82, 105, 115, 125 Ans: The second set of data can be obtained from the first set by adding 8 to each datum in the first set. The standard deviation of the second set is about 35. Difficulty: medium Page 4
11. One measure of center that sometimes is used is the midrange. To find the midrange, compute the mean of the largest value and the smallest value. Using the summary statistics show below, compute the mean of the data excluding the maximum value (which is an outlier). Variable N Mean Median TrMean StDev SeMean x 53 14.213 13.824 12.906 8.414 0.373 Min Max Q1 Q3 5.616 90.030 6.976 24.066 A) 12.755 B) 12.514 C) 5.799 D) 12.482 Ans: A Difficulty: medium 12. Suppose you have six pennies, twelve nickels, eleven dimes, and twenty quarters. Compute the mean using the formula for the mean of values in a frequency table. A) 12.250 B) 1.690 C) 0.141 D) 0.138 13. On the first test of the semester, the scores of the first-hour class of 34 students had a mean of 69 and a median of 67. The scores of the second-hour class of 32 students had a mean of 73 and a median of 71. To the nearest tenth, what is the mean test score of all 66 students? A) 71.0 B) 68.9 C) 70.9 D) 69.0 Ans: C Difficulty: medium Page 5
14. The cumulative relative frequency plot below shows the amount of change carried by a group of 200 students. a. From the plot, estimate the median amount of change. b. Estimate the quartiles and the interquartile range. c. Is the original set of amounts of change skewed right, skewed left, or symmetric? Ans: a. median = 130 b. Q1 = 80, Q3 = 160, IQR = 80 c. symmetric Difficulty: high Page 6
15. Match the histogram with its cumulative relative frequency plot. A) B) Page 7
C) D) Ans: A Difficulty: medium 16. What percentage of values in a standard normal distribution fall below a z-score of 1.6? A) 11.0% B) 94.5% C) 1.6% D) 5.5% 17. What percentage of values in a standard normal distribution fall between z-scores of 2.5 and 2.5? A) 99.4% B) 0.6% C) 49.4% D) 98.8% 18. Convert the value to standard units, z. x = 67, mean = 47, standard deviation = 4 A) 5 B) 27 C) 52 D) 42 Ans: A Difficulty: medium Page 8
19. Find the value of x that was converted to the given z-score. z = 1.5, mean = 45, standard deviation = 3 A) 49.5 B) 15.50 C) 43.5 D) 40.5 20. SAT I math scores are scaled so that they are approximately normal, with a mean about 519 and standard deviation about 114. A college wants to send letters to students scoring in the top 15% on the exam. What SAT I math score should the college use as the dividing line between those who get letters and those who do not? A) 643 B) 637 C) 630 D) 624 Ans: B Difficulty: medium 21. Find the missing value. Mean SD x Proportion (below value x) --- 2 40 0.40 A) 44.8 B) 49.3 C) 40.5 D) 53.6 Ans: C Difficulty: medium 22. Find the missing value. Mean SD x Proportion (below value x) 60 --- 51 0.40 A) 35.5 B) 33.9 C) 36.6 D) 41.4 Ans: A Difficulty: medium 23. Find the missing value. Mean SD Q1 Q3 80 8.0 --- --- A) Q1 = 72.0; Q3 = 88.0 C) Q1 = 76.0; Q3 = 84.0 B) Q1 = 74.6; Q3 = 85.4 D) Q1 = 73.3; Q3 = 86.7 Ans: B Difficulty: medium 24. A group of subjects tested a certain brand of foam earplug. The number of decibels (db) that noise was reduced for these subjects was approximately normally distributed, with mean 45 db and a standard deviation 5.3 db. The middle 90% of noise reductions were between what two values? A) 34.5 db and 55.5 db C) 38.2 db and 51.8 db B) 36.3 db and 53.7 db D) 39.7 db and 50.3 db Ans: B Difficulty: medium Page 9
25. The distribution of weights (in pounds) of adult beagles is approximately normal, with a mean of 22 lb. and a standard deviation of 3.2 lb. If there are about 23,000 adult beagles in the greater-metropolitan area, how many adult beagles will be between 18.7 lb. and 25.3 lb.? A) about 16,000 adult beagles C) about 20,000 adult beagles B) about 7000 adult beagles D) about 21,000 adult beagles Ans: A Difficulty: medium Page 10