Midterm Exam #1. Introduction to Statistics / MAT300 SPRING 2014 MYERS-MAT300041VA (Prof. Myers)

Transcription

1 Midterm Exam #1 Introduction to Statistics / MAT300 SPRING 2014 MYERS-MAT300041VA (Prof. Myers) Student Name/ID: 1. Which of the following variables are best thought of as continuous, which discrete? Indicate your choice for each by circling the appropriate answer. (a) In a reaction time study involving between and milliseconds. participants, the number of participants whose average time is Discrete Continuous (b) The lifetime, in hours, of a -watt light bulb manufactured by Northington Industries. Discrete Continuous (c) The time that a student in Calculus takes to complete a midterm exam. Discrete Continuous (d) The mass of the solid impurities per milliliter of Los Angeles tap water. Discrete Continuous ALEKS Midterm Exam #1-04/27/ :08:12 PM EDT -Copyright 2014 UC Regents and ALEKS Corporation. P. 1/13

2 2. The stem-and-leaf display below gives the fuel efficiencies (in miles per gallon) for a sample of new cars. Use the display to answer the following questions. Fuel efficiency (miles per gallon) Key: means a fuel efficiency of miles per gallon. (a) What is the lowest fuel efficiency in the sample overall? (b) What is the highest fuel efficiency in the sample in the 20s? (c) How many cars in the sample have fuel efficiencies in the 30s? ALEKS Midterm Exam #1-04/27/ :08:12 PM EDT -Copyright 2014 UC Regents and ALEKS Corporation. P. 2/13

3 3. A realtor is displaying the histogram below, which summarizes the percentage of appreciation in value (over the past five years) for each of a sample of houses in Newburg Park. Based on the histogram, find the proportion of appreciation percentages in the sample that are less than percent. Write your answer as a decimal, and do not round your answer. 4. The students of a certain college were asked to choose which of six movie genres was their favorite. The pie chart below shows the distribution of the students' answers. If there are students at this college, how many chose Action or Drama? ALEKS Midterm Exam #1-04/27/ :08:12 PM EDT -Copyright 2014 UC Regents and ALEKS Corporation. P. 3/13

4 5. The following are distances (in miles) traveled to the workplace by employees of a certain university. 7, 2, 37, 32, 27, 22, 16, 11, 6, 1, 36, 31, 10, 10, 10, 5, 5, 40. Draw the histogram for these data using an initial class boundary of, an ending class boundary of, and classes of equal width. Note that you can add or remove classes from the figure. Label each class with its endpoints. 6. Each year, taxpayers are able to contribute money to various charities via their IRS tax forms. The following list contains the amounts of money (in dollars) donated via IRS tax forms by taxpayers: 95, 95, 90, 86, 33, 51, 94, 21, 95. (a) What is the mean of this data set? If your answer is not an integer, round your answer to at least one decimal place. (b) What is the median of this data set? If your answer is not an integer, round your answer to at least one decimal place. (c) How many modes does the data set have, and what are their values? Indicate the number of modes by selecting the appropriate line, and then indicate the value(s) of the mode(s), if applicable. 1. zero modes 2. one mode: 3. two modes: ALEKS Midterm Exam #1-04/27/ :08:12 PM EDT -Copyright 2014 UC Regents and ALEKS Corporation. P. 4/13

5 7. The following are distances (in miles) traveled to the workplace by employees of a certain hospital. 25, 18, 14, 31, 11, 9. Find the standard deviation of this sample of distances. Round your answer to at least two decimal places. 8. Loretta, who turns eighty this year, has just learned about blood pressure problems in the elderly and is interested in how her blood pressure compares to those of her peers. Specifically, she is interested in her systolic blood pressure, which can be problematic among the elderly. She has uncovered an article in a scientific journal that reports that the mean systolic blood pressure measurement for women over seventy-five is mmhg, with a standard deviation of mmhg. Assume that the article reported correct information. Complete the following statements about the distribution of systolic blood pressure measurements for women over seventy-five. (a) According to Chebyshev's theorem, at least 84% of the measurements lie between mmhg and mmhg. (Round your answer to 1 decimal place.) (b) According to Chebyshev's theorem, at least % of the measurements lie between mmhg and mmhg. a. 56% b. 75% c. 84% d. 89% (c) Suppose that the distribution is bell-shaped. According to the empirical rule, approximately % of the measurements lie between mmhg and mmhg. a. 68% b. 75% c. 95% d. 99.7% (d) Suppose that the distribution is bell-shaped. According to the empirical rule, approximately 68% of the measurements lie between mmhg and mmhg. ALEKS Midterm Exam #1-04/27/ :08:12 PM EDT -Copyright 2014 UC Regents and ALEKS Corporation. P. 5/13

6 9. The following data are the grades of students on a statistics test. 94, 80, 66, 90, 74, 96, 76, 92, 66, 91, 61, 93, 83, 95, 89, 73, 97, 89. Construct a box-and-whisker plot for the data. ALEKS Midterm Exam #1-04/27/ :08:12 PM EDT -Copyright 2014 UC Regents and ALEKS Corporation. P. 6/13

7 10. Three distributions, labeled (a), (b), and (c), are represented below by their histograms. Each distribution is symmetrical and is made of measurements. Without performing any calculations, order their respective standard deviations,, and. 11. The scores on a test for a sample of statistics students are summarized in the following table. Number of students Score Find the mean score. Round your answer to at least one decimal place. 12. In how many ways can letters be chosen from, assuming that the order of the choices doesn't matter and that repeats are not allowed? (If necessary, consult a list of formulas.) ALEKS Midterm Exam #1-04/27/ :08:12 PM EDT -Copyright 2014 UC Regents and ALEKS Corporation. P. 7/13

8 13. As shown in the Venn diagram below, and are events in the sample space. Indicate the event by shading the appropriate region(s). 14. Suppose that and are independent events such that and. Find and. 15. At a factory that produces pistons for cars, Machine 1 produced satisfactory pistons and unsatisfactory pistons today. Machine 2 produced satisfactory pistons and unsatisfactory pistons today. Suppose that one piston from Machine 1 and one piston from Machine 2 are chosen at random from today's batch. What is the probability that the piston chosen from Machine 1 is satisfactory and the piston chosen from Machine 2 is unsatisfactory? Do not round your answer. ALEKS Midterm Exam #1-04/27/ :08:12 PM EDT -Copyright 2014 UC Regents and ALEKS Corporation. P. 8/13

9 16. Recently, Hector ran for president of the local school board. Of those who voted in the election, had a high school diploma, and the other did not. Hector got of the vote of those with high school diplomas, while he got only of the vote of those without high school diplomas. Let denote the event that a randomly chosen voter (in the school board election) had a high school diploma and denote the event that a randomly chosen voter did not have a high school diploma. Let denote the event that a randomly chosen voter voted for Hector and randomly chosen voter did not vote for Hector. denote the event that a Fill in the probabilities to complete the tree diagram below, and then answer the question that follows. Do not round any of your responses. 17. A catering service offers appetizers, main courses, and desserts. A banquet chairperson is to select appetizers, main courses, and desserts for a banquet. In how many ways can this be done? (If necessary, consult a list of formulas.) 18. An urn contains black and pink balls. Five balls are randomly drawn from the urn in succession, with replacement. That is, after each draw, the selected ball is returned to the urn. What is the probability that all balls drawn from the urn are black? Round your answer to three decimal places. ALEKS Midterm Exam #1-04/27/ :08:12 PM EDT -Copyright 2014 UC Regents and ALEKS Corporation. P. 9/13

10 19. A sample of adults is selected. The adults are classified according to their voter registration status and their preferred source of current events information. The results are given in the contingency table below. Voting registration status Preferred source of information Television Newspapers Radio Internet sites Registered Not registered What is the relative frequency of adults in the sample who prefer to obtain their information through television? Round your answer to at least two decimal places. 20. A pizza restaurant offers different toppings: of them are vegetarian and of them are non-vegetarian. A customer selects her first topping at random and then selects another one at random from the remaining toppings. What is the probability that both her selections are vegetarian? Report your answer as an exact fraction. ALEKS Midterm Exam #1-04/27/ :08:12 PM EDT -Copyright 2014 UC Regents and ALEKS Corporation. P. 10/13

11 Midterm Exam #1 Answers for class Introduction to Statistics / MAT300 SPRING 2014 MYERS-MAT300041VA (a) Discrete (b) Continuous (c) Continuous (d) Continuous 2. (a) What is the lowest fuel efficiency in the sample overall? (b) What is the highest fuel efficiency in the sample in the 20s? (c) How many cars in the sample have fuel efficiencies in the 30s? (a) What is the mean of this data set? If your answer is not an integer, round your answer to at least one decimal place. (b) What is the median of this data set? If your answer is not an integer, round your answer to at least one decimal place. (c) How many modes does the data set have, and what are their values? Indicate the number of modes by selecting the appropriate line, and then indicate the value(s) of the mode(s), if applicable. one mode: ALEKS Midterm Exam #1-04/27/ :08:12 PM EDT -Copyright 2014 UC Regents and ALEKS Corporation. P. 11/13

12 7. 8. (a) According to Chebyshev's theorem, at least 84% of the measurements lie between and mmhg. mmhg (b) According to Chebyshev's theorem, at least of the measurements lie between mmhg and mmhg. (c) Suppose that the distribution is bell-shaped. According to the empirical rule, approximately the measurements lie between mmhg and mmhg. (d) Suppose that the distribution is bell-shaped. According to the empirical rule, approximately the measurements lie between mmhg and mmhg. of of ALEKS Midterm Exam #1-04/27/ :08:12 PM EDT -Copyright 2014 UC Regents and ALEKS Corporation. P. 12/13

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