ST 511 ReilandMIDTERM EXAM PRACTICE PROBLEMSMaterial covered on exam: 9 all topics covered to this point in the course including random variables, ,IÐ\ÑZ+<Ð\Ñßand the algebra of expected values and variance not9the material on geometric, binomial, and Poisson distributions will be includedon the exam webassign homework #1 through #59 Important Note: This sample exam does not necessarily have a question for every topic that is included on themidterm exam.1. The heights of American men aged 18 to 24 are approximately symmetrically mound shaped with mean 68 inches and standard deviation 2.5 inches. Half of all young men are shorter than what height?2. Use the information in Problem 1. Use the 68-95-99.7 rule to determine the percentage of young men thatare taller than 6' 1" ?3. The grade point averages (GPA) of 7 randomly chosen students in a statistics class are3.14 2.37 2.94 3.60 1.70 4.00 1.85If ( 4.51, what is the standard deviation?!xx) œ#4. A survey conducted in a college stats class asked students about the number of credit hours they were takingthat semester. The number of credit hours for a random sample of 16 students is: 10 10 12 14 15 15 15 1517 17 19 20 20 20 20 22a. find the mean and standard deviation for the number of credit hours.b. find the median and IQR for the number of credit hours.c. is it more appropriate to use the mean and standard deviation or the median and IQR to summarize thesedata?5. A standardized test designed to measure math anxiety has a mean of 100 and a standard deviationof 10 in the population of first year college students. Which of the following observations wouldyou suspect is an outlier? a) 150 b) 100 c) 90 d) 125 e) none of the above6. Twenty-eight applicants interested in working for the Food Stamp program took an examination designed tomeasure their aptitude for social work. The following test scores were obtained:79, 93, 84, 86, 77, 63, 46, 97, 87, 88, 87, 92, 68, 72, 86, 98, 81, 70, 66, 98, 59, 76, 68, 91, 94,85, 88, 79.a. Find , the first quartile. U"b. Construct a boxplot for these observations. Do you observe any outliers?7. The boxplots show the age of people involved in traffic-related accidents according to their role in theaccident.ST 511 Midterm Exam Practice Problems page 2 a. Which role involved the youngest person, and what is the age? , b. Which role had the lowest median, and what is the age? , c. Which role had the smallest range of ages, and what is it? , d. Which role had the largest IQR of ages, and what is it? , e. Which role generally had the oldest people?8. A manufacturer of television sets has found that for the sets he produces, the lengths of time until the firstrepair can be described using a normal model with a mean of 4.5 years and a standard deviation of 1.5 years.If the manufacturer sets the warrantee so that only 10.2% of the 1st repairs are covered by the warrantee,how long should the warrantee last?9. Suppose the amount of tar in cigarettes can be described using a normal model with a mean of 3.5 mg and astandard deviation of 0.5 mg.a. What proportion of cigarettes have a tar content that exceeds 4.25 mg?b. In order to advertise as a low tar brand, a manufacturer must prove that their tar content is below the 25thpercentile of the tar content distribution. Find the 25th percentile of the distribution of tar amounts.10. The mean SAT verbal score of next year's freshmen entering the local university is 600. It is also knownthat 69.5% of these freshmen have scores that are less than 625. If the scores can be described using anormal model, what is the standard deviation of the scores?11. Two students are enrolled in an introductory statistics course at the University of Florida. The first studentis in a morning section and the second student is in an afternoon section. If the student in the morningsection takes a midterm and earns a score of 76, while the student in the afternoon section takes a midtermwith a score of 72, which student has performed better compared to the rest of the students in his respectiveclass? Assume that the test scores follow a normal model. For the morning class, the class mean was 64with a standard deviation of 8. For the afternoon class, the class mean was 60 with a standard deviation of7.5.12. The following data are a sample of the percentage rates of return experienced by six-month Eurodollardeposit purchasers:1 2 2 1 1 4 2 3 1ST 511 Midterm Exam Practice Problems page 3The standard deviation is: a. 4 b. 2 c. 1.05 d. 1.11 e. can't be done since some values are negative13. The highway gas mileage , measured in miles per gallon (mpg), of 26 models of midsize cars, have theBfollowing summary statistics: 26.54 mpg, median 26 mpg, 3.04 mpg, 3 mpg. If youBœ œ =œ œIQRconvert gas mileage from miles per gallon to which is measured in miles per liter, what are the newBB8/Avalues of the summary statistics? (3.785 liters 1 gallon).œ14. Shown below is the normal probability plot for 200 monthly telephone bills.Normal Quantile Plot02040608010 012 014 0-4 -3 -2 -1 0 1 2 3 4z-scorephone bills Shown below is a histogram. Is this a histogram of the same data that was used to construct the normalprobability plot?Histogram010203040Frequency 15. A local plumber makes house calls. She charges $30 to come out to the house and $40 per hour for herservices. For example, a 4-hour service call costs $30 + $40(4) = $190. a. The table shows summary statistics for the length of service calls for the past month. Fill in the table tofind out the cost of the service calls. 4.53.51.22.00.5Statistic Hours of Service Call Cost of Service CallMeanMedianStan DevIQRMinimum b. This past month, the time the plumber spent on a particular service call had a z-score of 1.50. Whatis the z-score for the cost of the service call?16. In 2000 the Department of Education published the Digest for Education Statistics, a collection ofinformation about education in the United States. They reported the average amount (dollars per student)ST 511 Midterm Exam Practice Problems page 4spent by public schools in each state and Washington, D.C.during the school year 1997-8. The data wasrecorded according to whether the state lies east or west of the Mississippi River. A back-to-back stem andleaf display of the data is shown below. 6 7 denotes