Chapters 1 & 2 Exam Review

Transcription

1 Problems 1-3 refer to the following five boxplots. 1.) To which of the above boxplots does the following histogram correspond? (A) A (B) B (C) C (D) D (E) E 2.) To which of the above boxplots does the following histogram correspond? (A) A (B) B (C) C (D) D (E) E 3.) To which of the above boxplots does the following histogram correspond? (A) A (B) B (C) C (D) D (E) E

2 4.) Which of the following will most likely approximate a uniform distribution? (a) heights of students at a particular high school (b) weights of students at a particular high school (c) SAT scores of seniors at a particular high school (d) IQ scores of students at a particular high school (e) ages of students at a particular high school 5.) A reporter wishes to portray baseball players as overpaid. Which measure of center should he report as the average salary of major league players? (a) The mean. (b) The median. (c) The mode. (d) Either the mean or median. It doesn t matter since they will be equal. (e) Neither the mean nor median. Both will be much lower than the actual average salary. 6.) The SAT math scores for an AP Statistics class of 20 students are listed below: 664, 658, 610, 670, 640, 643, 675, 650, 676, 575, 660, 661, 520, 667, 668, 635, 671, 673, 645, 650 The distribution of scores is (a) symmetric (b) skewed to the left (c) skewed to the right (d) uniform (e) bimodal 7.) The 60 longest rivers in the world have lengths distributed as follows: Length (miles) # of Rivers (The Nile is the longest with a length of 4145 miles, and the Amazon is the second longest at 3900 miles) Which of the following best describes the data? (a) Skewed distribution, mean greater than median (b) Skewed distribution, median greater than mean (c) Symmetric distribution, mean greater than median (d) Symmetric distribution, median greater than mean (e) Symmetric distribution with outliers on high end

3 8.) Which of the following is a resistant measure? (a) mean (b) median (c) standard deviation (d) range 9.) Consider the following back-to-back stemplots comparing car battery lives (in months) of samples of two popular brands represents 47 for Brand A and 42 for Brand B Which of the following are true statements? I. The sample sizes are the same II. The ranges are the same III. The variances are the same IV. The means are the same V. The medians are the same (a) I and II (b) I and IV (c) II and V (d) III and V (e) I,II and III 10.) Which statement is true about the boxplot below? I. It is a left skewed distribution which has outliers II. It is a symmetrical distribution which has outliers III. The interquartile range (IQR) is less than 1 IV. Approximately 75% of the observations have a GPA less than 3 (a.) I only (b) II only (c) II and III (d) III ad IV only (e) I, III and IV

4 11. Which of the following are true statements? I. The area under a normal curve is always 1, regardless of the mean and standard deviation. II. The mean is always equal to the median for any normal distribution. III. The interquartile range for any normal curve extends from µ 1σ to (a) I and II (b) I and III (c) II and III (d) I, II, and III (e) None of the above gives the correct set of true responses. µ + 1σ 12. Pop1 and Pop2 are normal density curves with means and standard deviations µ 1, σ 1 and µ 2, σ 2, respectively. Suppose that µ 1 = µ 2 and σ 1 = 2(σ 2 ). Consider these statements: I. Pop1 has twice as many observations within one standard deviation as Pop2. II. The density curve for Pop1 is taller than that of Pop2. III. The density curves are centered around different numbers. Which of these statements are correct? (a) I only (b) II only (c) III only (d) I and II only (e) None of the above gives the correct set of true responses. 13. The distribution of actual weights of 8.00 ounce chocolate bars produced by a certain machine is normal with a mean of 8.10 ounces and a standard deviation of 0.10 ounces. The proportion of chocolate bars weighing between 8.25 and 8.35 ounces is (a) (b).0606 (c).9332 (d).9938 (e) none of the above 14. This is a continuation of Question 13. Approximately what proportion of the chocolate bars will be greater than 8.33 ounces in weight? (a).0107 (b).0250 (c).9750 (d).9893 (e) none of the above

5 15.) The boxplots above summarize two sets of data, X and Y. Which of the following must be true. I. Set Y contains more observations than Set X II. Set X has a larger range than Set Y III. Set X and Y have the same median (a) I only (b) III only (c) I and II only (d) II and III only (e) I, II and III 16.) Based on the chart of test scores below, the class that contains the 20 th percentile is? (a) (b) (c) (d) (e) there is not enough information to answer this question 17.) Below is the performance of fourth grade boys and girls on an agility test. The test asked them to jump from side to side across a set of parallel lines, counting the number of lines they can clear in 30 seconds. Graph comparative boxplots of the data, and then write a summary comparing the distributions. Boys: 22, 17, 18, 29, 22, 22, 23, 24, 23, 17, 21 Girls: 25, 20, 12, 19, 28, 24, 22, 21, 25, 26, 25, 26, 27, 22

6 18.) Derby Speeds How fast do horses run? Kentucky Derby winners top 30 miles per hour, as shown in the ogive below. In fact, this graph shows the percentage of Derby winners that have run slower than a given speed. Note that a few have won running less than 33 miles per hour, but about 95% of the winning horses have run less than 37 miles per hour. a. Estimate the median winning speed. b. Estimate the quartiles c. Estimate the interquartile range (IQR) d. Estimate the range 19. (a) In your own words, describe what the standard deviation measures. (b) By hand, calculate the sample standard deviation of the data set 6,5,4,10,9,13, 7. Show your work. (c) Make up a data set with a mean of 9 and a standard deviation of 2.

7 20.) Find the number z such the proportion of observations that are less than z in a standard normal distribution is ) Find the number z such that 22% of all observations from a standard normal distribution are greater than z. 22.) The distribution of blood cholesterol levels for 14 year old boys vary normally with a mean of 170 mg/dl and standard deviation 30 mg/dl. Find the quartiles for this distribution. 23.) An important measure of the performance of a locomotive is its adhesion which is the locomotive s pulling force as a multiple of its weight. The adhesion of one 4400 horsepower diesel locomotive model varies in actual use according to a normal distribution with a mean µ = 0.41 and a standard deviation σ = 0.02 (a) What proportion of adhesions measured in use are higher than 0.40? (b) What proportion of adhesions are between 0.40 and 0.50? 24. The army reports that the distribution of head circumferences among soldiers is approximately normal with mean 22.8 inches and standard deviation 1.1 inches. Helmets are mass produced for all except the smallest 5% and the largest 5% of head sizes. Soldiers in the largest or smallest 5% get custom-made helmets. What head sizes get custom made helmets?

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