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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 6893993 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 HarvesterForwarder Softwood
Thinning” (Forest Pmducts J., May 1997: 3641). 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
RSq 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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 Summer '08
 NANE

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