practice-exam1-421-summer08

practice-exam1-421-summer08 - l. Fifty applicants...

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Unformatted text preview: l. Fifty applicants interested in working for the Food Stamp program took examination designed to measure their a I ptitude for social work. Below is the relati've'freQuency histogram for the scores data. - ' I _ ' a. (7 pts.) Find the missing height mrer (70,80) and restore the frequency table for it your frequency table- i550).' ("lake sure that the total number of entries in b. (3 pts.) It is knew): that if a histogram is pesitively skewed, then (normally) the mean is greater than the median, while if it“- is negatively skewed, then the median is larger.' Can you compare the median with the mean for the given histogram? Which one is greater? 2. Given the (artificial) data set 10, 2, 16, 6, O, 8, 2, 6, 6, 8 a. (6:2+2+2 pts.) Calculate Qi,M,Q3 (first and third quartiles and median). 3* 'b. (6:3+3 pts-) Calculate the interquartile range (IQR) and point out outliers, if any (use the 1.5x IQR criterion). " 3. (7 pts.) Create a set of 5 positive numbers (repeats allowed) that have median 10 and mean 7. 4. (7221—5 pts.) For the following small data set. Calculate mean 5 and standard deviation 3,. 7. The length of horse pregnancies from conception to birth varies accurrlinp; to a roughly normal distribution with mean 336 days and standard deviation 3 days. Use the 68-93993 rule to answer the following questions. a. {6 pts-) Almost all (99.7%)horse pregnancies fall in what range of lengths? I). (7 pts.) What percent. of horse pregnancies are longer than 339 days? 8. Using Table A find the proportion of observation frmn a standard 110111131 distribution for each of the following events. a. (5 pts-) Z > 1.67 . b. (6 pts.) ——2 < Z <; 1.67 9- Find the value 3 of standard normal variable 71 that satisfies each of the following conditions. (Report the value of z that comes closest to satisfying the condition.) In each case, sketch :1 standard normal curve’yvith your value of z marked on the axis. a. (6 pts.) 20% of the observations fall below 2. b. (6 pts.) 30% of the observations fall above .3. 10. The diameter (in inches) at breast height of trees of certain type is normally distributed with ,u = 8.8 and 0' = 2.8 as suggested in the article "Simulating a Harvester-Forwarder Softwood Thinning” (Forest Pmducts J., May 1997: 36-41). a. (7 pts.) What proportion of tree diameters fall between 8.0 and 9.5 in? b. (8 pts.) What diameter value separates the largest 75% of all tree diameters from the others? e. Extra credit (7 pts.) Between What. values do the diameters of the middle 75 % of all trees fall? \ 11. (9 pts.) Establish the correspondence between the scatterplots below and their (rear- "_Iranged) correlations: r = —.7, r z 0, r = .5, r = ——.3, r : .9, r 2 ~39 . 12. There is some evidence that drinking [moderate alnount. of wine helps prevent heart attacks. The scatterplot below provided by MINI’.I.‘AB gives data on yearly wine consumption (liters of alcohol from drinking wine per person (horizontal axis”, and yearly deaths from heart disease (deaths per 100,000 population) in 19 developed nations. I 37.3 R-Sq 71.0% . R—Sq(adj) 69.3% a. {6 pts.) According to the above printout, r2 — .T] . \Nllal. is the value ol'r? b. (6 pts-) Use the abovo‘lequatinn 0f the least squares [aggression line to predict the value of the heart disease deaths for the value :: : 3.2 liters- 13. Consolidated Builders has bid on two large construction projects. The company president believes that the probability of Winning the first contract (event A) is 0.6, that the probability of winning the second (event B) is 0.5, and that the probability of winning both jobs (event {AandB} is 0.3. Use standard operations to express each of the following events in terms of A , B, A“ , and Bc , and find their probability. For each of the events draw the Venn diagram: and 5hudc the event in qllnstiuh. a. (5 pts.) Consolidated wins at least one of the jobs? b. (5 pts-) Consolidated wins both jobs. c. (5 pts.) Consolidated wins the first job, but not the second. (1. (5 pts.) Consolidated does not win the first job, but does win the second. e. (5 pts.) Consolidated does not win either job. 14. In a certain population of voters 60 % are Republicans and 40% are Democrats. It is reported that 30% of the Republicans aiid 80% of Democrats favor a certain election issue- a. (7 pts.) Find the probability that a voter chosen at random from this population favors the issue in question. (Use either the Venn diagram , or the tree diagram technique.) ...
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practice-exam1-421-summer08 - l. Fifty applicants...

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