test 4 review 1010 SHORT ANSWER. Write the word or phrase that best completes each statement or answers the question. Use the given data to construct a frequency and relative frequency distribution. 1) Kevin asked some of his friends how many hours they had worked during the previous week at their after-school jobs. The results are shown below. 6 5 6 4 6 6 9 8 6 4 8 5 5 8 6 5 8 6 5 8 5 8 8 4 Construct a frequency and relative frequency distribution. Use 4 classes. Find the area under the normal curve for the condition. 7) Find the percent of the area under the curve between the mean and 3.01 standard deviations from the mean. Use the standard normal curve table to find the closest z-score for the given condition. 8) 74.9% of the total area is to the left of z. A company installs 5,000 light bulbs. The lifetimes of the lightbulbs are approximately normally distributed with a mean of 500 hours and a standard deviation of 100 hours. Find the approximate number of bulbs that can be expected to last the indicated amount of time. 9) More than 740 hours Find the mean of the set of data. 2) 3.5 1.6 2.4 3.7 4.1 3.9 1.0 3.6 4.2 3.4 3.7 2.2 1.5 4.2 3.4 2.7 0.4 3.7 2.0 3.6 Round your answer to two decimal places. Find the range for the set of data given. 3) 117 527 136 607 404 237 Solve the problem. 4) At Loop Junior College, the mean grade point average (gpa) of the current student body is 2.76 with a standard deviation of 0.64. Compute the gpa's of each student to two decimal places. A gpa with a z-score of 0.6. A gpa with a z-score of -1.2. Classify the random variable as either discrete or continuous. 5) The number of colleges in a state At one high school, the mean time for running the 100-yard dash is 15.2 seconds with a standard deviation of 0.9 seconds. The times are very closely approximated by a normal curve. Find the percent of times that are: 6) Between 15.2 and 16.1 seconds Find the indicated probability or percentage for the normally distributed variable. 10) A machine produces pencils with a mean diameter of 0.30 inches and a standard deviation of 0.01 inches. The diameters are approximately normally distributed. What is the probability that a randomly selected pencil has a diameter less than 0.285 inches? Solve the problem. 11) Scores on a test are approximately normally distributed with a mean of 70 and a standard deviation of 9. The teacher wants to give A's to the top 10% of students, B's to the next 25%, and C's to the next 42%. What is the bottom cutoff for a C grade? Round your answer to the nearest whole number. 12) At Loop College, the mean grade point average (gpa) of the current student body is 2.76 with a standard deviation of 0.64. Find the gpa of a student whose z-score is -2.8. Round to the nearest hundredth. Rank the data from lowest to highest and determine the requested quartile. 13) The following scores on the midterm exam in Chemistry 102 were recorded. 93 81 59 69 82 74 61 77 95 84 88 71 85 97 63 72 89 80 60 98 91 62 78 83 76 81 94 66 83 96 Find the 1st quartile, Q1. 1
Find the indicated decile or percentile. 14) The test scores of 19 students are listed below. Find the sixth decile, D6. Solve. 15) 36 45 49 53 55 56 59 61 62 65 68 70 74 78 84 88 91 92 99 Provide an appropriate response. 20) We want to compare two different groups of students, students taking Composition 1 in a traditional lecture format and students taking Composition 1 in a distance learning format. We know that the mean score on the research paper is 85 for both groups. What additional information would be provided by knowing the standard deviation? Find the median. 21) 31, 14, 7, 5, 24, 12, 29, 31, 40, 35 Find the mode or modes. 22) 7.07, 7.41, 7.56, 7.07, 7.88, 7.99, 7.62 Give the median of the data set represented by the box plot above. True or false? 16) A person who scored at the eightieth percentile in a test answered eighty percent of the questions correctly. Find the standard deviation. Round to one more place than the data. 17) 2, 3, 16, 18, 6, 19, 11, 18, 17 Use Chebyshev's theorem to solve the problem. 18) In a certain distribution of numbers, the mean is 50 and the standard deviation is 6. What can you say about the percentage of numbers that lie between 29 and 71? Find the standard deviation for the given data. Round your final answer to one more decimal place than that used for the observations. 19) Christine is currently taking college astronomy. The instructor often gives quizzes. On the past seven quizzes, Christine got the following scores. 51 20 114 25 10 46 58 Find the mean for the given frequency distribution. 23) Value Frequency 12 2 17 12 22 20 31 13 33 10 Find the median for the given frequency distribution. Value Frequency 60 4 62 8 24) 64 12 66 20 68 31 70 13 Find the mean for the given sample data. Unless otherwise specified, round your answer to one more decimal place than that used for the observations. 25) Last year, nine employees of an electronics company retired. Their ages at retirement are listed below. Find the mean retirement age. 56 67 63 55 68 58 61 50 54 2
Find the median for the given sample data. 26) The weights (in ounces) of 21 cookies are shown. Find the median weight. 0.72 1.26 0.80 1.62 0.86 0.60 1.09 1.26 1.53 0.95 0.72 1.45 1.03 0.80 0.47 1.45 0.60 1.03 1.72 0.86 0.56 Solve the problem. 27) Jackie's sisters weigh 117 lb, 148 lb, 128 lb, and 125 lb. The average female in her city weighs 139.1 lb. How much does Jackie weigh if she and her sisters have an average weight of 139.1 lb? Construct a frequency polygon. 30) Number of vacation days Number of employees 1-5 10 6-10 25 11-15 35 16-20 20 21-25 10 Provide an appropriate response. 28) The median of a data set is always/sometimes/never (select one) one of the data points in a set of data. Explain your answer with brief examples. Construct the specified histogram. 29) The ages of the voters at a poll during a 20-minute period are listed below. Use five classes with a uniform width of 10 years, where the lower limit of the first class is 20 years. 35 29 48 63 64 38 21 23 41 68 61 42 43 47 33 37 46 27 23 30 Construct a stem and leaf display for given data. 31) Mr. Johnson wants to display his employees' ages in a graph. Below are their ages. 23 36 45 42 34 53 34 27 24 Use this graph to answer the question. Big "D" Sales for 2009, 2010 Sales (thousands of dollars) 2010 2009 Month 32) What month in 2010 had the lowest sales? 3
Answer the question. 33) The bar graph below shows the number of students by major in the College of Arts and Sciences. In a school survey, students showed these preferences for instructional materials. Answer the question. MAJOR Did twice as many students major in English as in Math? This double-bar graph shows the number of male (M) and female (F) athletes at a university over a four-year period. Answer the question. 35) How many degrees are in the central angle for the "Lecture" sector? Use the information to complete a circle graph. Note that the circle is divided into 100 equal sections. 36) Main form of exercise for employees of one company: None: 30% Walking: 18% Running: 4% Golf: 11% Weight Training: 26% Other: 11% YEAR 34) Which year had the smallest number of female athletes? 4
Use the graph to answer the question. 37) Make a bar graph to represent the data. 40) Construct a vertical bar graph for the relative frequencies given. Blood Frequency Relative type frequency O 22 0.44 A 19 0.38 B 6 0.12 AB 3 0.06 Mike decides to buy shares of companies A, B, and C, which were initially selling for the same price. The changes in each stock's value are shown in the graph above. At its peak, stock A was valued at approximately how much more than either B or C? Solve the problem. 38) Sixteen workers were surveyed about how long it takes them to travel to work each day. The data below are given in minutes. Represent the data in a double-stem display. 20 35 42 20 24 37 23 24 22 20 41 25 28 27 30 32 Find the indicated probability. 39) A relative frequency distribution is given below for the size of families in one U.S. city. Size Relative frequency 2 0.448 3 0.208 4 0.203 5 0.094 6 0.029 7+ 0.018 Provide an appropriate response. 41) Shortly before a mayoral election, a market research firm took a poll to find out which candidate people were planning to vote for. The results are shown below. Candidate Frequency Li Fong 2120 Bob Green 2329 Sue Moore 1042 Jose Alvarez 399 You wish to construct a graph to represent the data. It should be easy to see from your graph which candidate is in the lead. Which graph would be more useful, a bar graph or a pie chart? Explain your thinking. A family is selected at random. Find the probability that the size of the family is between 2 and 5 inclusive. Round your answer to three decimal places. 5
Answer Key Testname: UNTITLED1 1) Hours Frequency Relative Frequency x f f/n 3-4 3 3/24 13% 5-6 13 13/24 54% 7-8 7 7/24 29% 9-10 1 1/24 4% 2) 2.94 3) 490 4) 3.14, 1.99 5) Discrete 6) 34% 7) 49.9% 8) 0.67 9) 40 10) 0.067 11) 63 12) 0.97 13) 71 14) 70 15) 35 16) False 17) 6.9 18) at least 91.8% 19) 34.7 20) Answers will vary. Possible answer: The standard deviation will give an indication of how widely the scores vary. More precisely, it gives an indication of how much the scores deviate, on average, from the mean score of 85. 21) 26.5 22) 7.07 23) 24.6 24) 67 25) 59.1 26) 0.95 ounces 27) 177.5 lb 28) Answers will vary. Possible answer: The median is sometimes one of the data points. If the number of data points is odd, the median will be one of the data points (the middle data point). If the number of data points is even, the median is the average of the two middle data points which will be equal to one of the data points only if the two middle data points are identical. 6
Answer Key Testname: UNTITLED1 29) 30) Frequency 31) 2 347 3 446 4 25 5 3 32) Month 2 33) Yes 34) 1986 35) 64.8 36) Number of vacation days 37) $35 38) (20-24) 2 (25-29) 2 (30-34) 3 (35-39) 3 (40-44) 4 39) 0.953 0 0 0 2 3 4 4 5 7 8 0 2 5 7 1 2 7
Answer Key Testname: UNTITLED1 40) 41) Answers will vary. Possible answer: A bar graph would be more useful. A bar graph is useful for comparing the sizes of different categories with each other, since it is easy to compare the heights of different bars. 8