Math Statistics & Probability Instructor: Dalip Sondhi Exam 1
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1 Math Statistics & Probability Instructor: Dalip Sondhi Exam 1 Name Date: Please submit this test with your answers summarized on it. Also staple to it your work done neatly on separate sheets showing explanations. Submit a scantron as well. For problem 31: Determine outliers & indicate with dots. The minimum and maximum positions will be replaced by Q1-1.5 IQR and Q IQR. MULTIPLE CHOICE. Choose the one alternative that best completes the statement or answers the question. Classify the study as either descriptive or inferential. 1) The table below shows the average income by age group for the residents of one town in the year The average incomes for each age group are estimates based on a sample of size 100 from each group. 1) Age group Average income $17, $26, $32, $25,960 Over 70 $18,241 A) Descriptive B) Inferential Determine which of the four levels of measurement (nominal, ordinal, interval, ratio) is most appropriate. 2) The sample of spheres categorized from softest to hardest. A) Nominal B) Ratio C) Ordinal D) Interval Identify which of these types of sampling is used: random, stratified, systematic, cluster, convenience. 3) A market researcher selects 500 people from each of 10 cities. A) Stratified B) Systematic C) Random D) Cluster E) Convenience Identify the study as an observational study or a designed experiment. 4) A doctor performs several diagnostic tests to determine the reason for a patient's illness. A) Designed experiment B) Observational study 2) 3) 4) 1
2 Solve the problem. 5) Using the employment information in the table on Alpha Corporation, find the class boundaries for class ) Years employed at Alpha Corporation Class Limits (years of service) Frequency (No. of employees) A) 25.5, 20.5 B) 26.5, 29.5 C) 25.5, 30.5 D) 26.5, 30.5 Construct the relative frequency distribution that corresponds to the given frequency distribution. 6) <61 2 A) Relative % % % % < % C) Relative % % % % < % B) Relative % % % % < % D) Relative % % % % < % 6) 2
3 Construct the cumulative frequency distribution that corresponds to the given frequency distribution. 7) Height (inches) Frequency ) A) Height (inches) Cumulative Frequency C) Height Cumulative (inches) Frequency B) Height (inches) Cumulative Frequency D) Height Cumulative (inches) Frequency A nurse measured the blood pressure of each person who visited her clinic. Following is a relative-frequency histogram for the systolic blood pressure readings for those people aged between 25 and 40. Use the histogram to answer the question. The blood pressure readings were given to the nearest whole number. 8) Approximately what percentage of the people aged had a systolic blood pressure reading between 110 and 119 inclusive? A) 0.35% B) 3.5% C) 35% D) 30% 8) 3
4 9) Approximately what percentage of the people aged had a systolic blood pressure reading between 110 and 139 inclusive? A) 59% B) 39% C) 75% D) 89% 10) What common class width was used to construct the frequency distribution? A) 9 B) 11 C) 10 D) ) Identify the center of the third class. A) 124 B) 125 C) 130 D) 120 Use the circle graph to solve the problem. 12) The circle graph below gives the inventory of the women's department of a store. 9) 10) 11) 12) Coats $49,737 Dresses $47,208 Skirts Lingerie $9273 $5058 Slacks Socks $15,174 Blouses $2529 $5901 What is the total inventory? A) $137,409 B) $132,351 C) $87,672 D) $134,880 Find the original data from the stem-and-leaf plot. 13) Stem Leaves A) 7, 14, 7, 7, 10, 11, 9, 9, 12, 16, 17, 13, 13, 15 B) 61, 68, 71, 71, 74, 75, 81, 84, 84, 88, 89, 94, 94 C) 61, 68, 74, 74, 75, 84, 84, 88, 89, 94, 94 D) 64, 64, 64, 71, 71, 74, 75, 81, 81, 94, 94 13) 4
5 Construct a pie chart representing the given data set. 14) The following figures give the distribution of land (in acres) for a county containing 74,000 acres. Forest Farm Urban 11, ,500 14) A) B) Find the mean for the given sample data. 15) The normal monthly precipitation (in inches) for August is listed for 20 different U.S. cities. Find the mean of the data A) 2.94 in. B) 3.27 in. C) 3.09 in. D) 2.80 in. Find the median for the given sample data. 16) The number of vehicles passing through a bank drive-up line during each 15-minute period was recorded. The results are shown below. Find the median number of vehicles going through the line in a fifteen-minute period A) 27 B) 30 C) D) 26 Find the mode(s) for the given sample data. 17) The speeds (in mi/h) of the cars passing a certain checkpoint are measured by radar. The results are shown below A) 44.6 B) 43.6 C) 43.6, 42.5, 44.6 D) ) 16) 17) 5
6 Solve the problem. 18) A car dealer is deciding what kinds of vehicles he should order from the factory. He looks at his sales report for the preceding period. Choose the vertical scale so that the relative frequencies are represented. Vehicle Sales Economy 28 Sports 7 Family 49 Luxury 14 Truck 42 Construct a Pareto chart to help him decide. A) B) 18) C) D) Find the midrange for the given sample data. 19) A meteorologist records the number of clear days in a given year in each of 21 different U.S. cities. The results are shown below. Find the midrange A) 117 B) 112 C) 98 D) ) 6
7 Find the mean of the data summarized in the given frequency distribution. 20) The heights of a group of professional basketball players are summarized in the frequency distribution below. Find the mean height. Round your answer to one decimal place. 20) Height (in.) Frequency A) 75.4 in. B) 78.2 in. C) 76.8 in. D) 13.5 in. Solve the problem. 21) Elaine gets quiz grades of 61, 76, and 77. She gets a 70 on her final exam. Find the weighted mean if the quizzes each count for 20% and the final exam counts for 40% of the final grade. A) 70.7 B) 71 C) 70.8 D) 69 Find the range for the given data. 22) The manager of an electrical supply store measured the diameters of the rolls of wire in the inventory. The diameters of the rolls (in m) are listed below Compute the range. A) B) C) D) Find the variance for the given data. Round your answer to one more decimal place than the original data. 23) Compute the variance. A class of sixth grade students kept accurate records on the amount of time they spent playing video games during a one-week period. The times (in hours) are listed below: A) B) C) D) ) 22) 23) Find the standard deviation for the given data. Round your answer to one more decimal place than the original data. 24) The manager of a small dry cleaner employs six people. As part of their personnel file, she asked each one to record to the nearest one-tenth of a mile the distance they travel one way from home to work. The six distances are listed below: Compute the standard deviation s. A) B) 6.48 C) D) ) 7
8 Find the range, variance, and standard deviation for each of the two samples, then compare the two sets of results. 25) When investigating times required for drive-through service, the following results (in seconds) were obtained. 25) Restaurant A Restaurant B A) Restaurant A: 57; ; Restaurant B: 56; ; C) Restaurant A: 75; ; Restaurant B: 70; ; B) Restaurant A: 57; ; Restaurant B: 70; ; D) Restaurant A: 57; ; Restaurant B: 77; ; Find the standard deviation of the data summarized in the given frequency distribution. 26) The manager of a bank recorded the amount of time each customer spent waiting in line during peak business hours one Monday. The frequency distribution below summarizes the results. Find the standard deviation. Round your answer to one decimal place. 26) Waiting time (minutes) Number of customer A) 7.0 B) 5.2 C) 5.0 D) 4.7 Find the percentile for the data point. 27) Data set: ; data point 52 A) 50 B) 57 C) 20 D) 43 Find the indicated measure. 28) The test scores of 40 students are listed below. Find P A) 74 B) 22.4 C) 73.5 D) 73 29) The test scores of 32 students are listed below. Find Q A) 79 B) 24 C) 79.5 D) 80 27) 28) 29) 8
9 Construct a boxplot for the given data. Include values of the 5-number summary in all boxplots. 30) The ages of the 35 members of a track and field team are listed below. Construct a boxplot for the data set A) B) 30) C) D) Construct a modified boxplot for the data. 31) The weights (in ounces) of 27 tomatoes are listed below. Construct a modified boxplot for the data. 31) A) B) C) D) 9
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