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Unformatted text preview: More Practice—STA 309 Spring 2009 Dr. Gemberling 1 Suppose you are the merchandise manager for Tiffany‘s Diamonds (an enviable position). You
wish to analyze the proﬁt margin of your diamonds based upon a sample of recentty—soid diamonds. If the average profit margin for the diamonds is in the lowest 5% of expected averages. you plan to
recommend entering higher proﬁt markets such as highend watches. You collect cost and sales data
for 190 diamonds and ﬁnd the mean profit margin for this sample is 23%. Historically. the mean profit
margin has been 25% with a standard deviation of 14%. a Where does your sample mean proﬁt margin lie in relation to the distribution of sample mean proﬁt margins for sampl of 190 diamonds? —
by” n=r‘io (744% z:%q‘33dﬁ :79?
  , _ X4390 /n* "two" '
“435], 1422390
=73? b. Based n your answer to part a, what will be your recommendation regarding entering the high and watch market? M Wm M . 2. A soft drink machine is regulated so that it discharges an average of p ounces per cup. if the
ounces of fill are normally distributed with a standard deviation of .4 ounces. what value should 1:. be
set at so that Bounce cups will overﬂow only 2% of the time? _ 2A2!
.01“ L} 0' . a .. __ a
1.1. x=g +;.05;(L,g 31$ng
5/ a 22:21.05 . ‘f r
3. The temperature at a in u rn the manufacture of bricks is normally distributed with a mean of
1000 degrees and a standard deviation of 50 degrees. if bricks are fired at temperatures above 1125
degrees. they will Crack and must be discarded. ﬂ : 1 pg 0 (5: 5 O a. What percent of bricks will be discarded? Amoco are; r 25: t= :2 . ‘3
b What percent of bricks will be ﬁred at under 900 degrees? 2;: 400 ' £00 x. 49_ race c Thirty percent of 11136136 will be ﬁred beiow what ﬁring temperature?
6030 X 7. M + 2'5"
: r000 ' 5250) '1 WELT 4. The time to complete a standardized exam is approximateiy normal with a mean of 70 minutes and
a standard deviation of 10 minutes. a. What cent of students will complete the exam in under an hour? 6515410 [512ch bd'OlUM 309.4197 VI M10 “‘70 to r
b. What percent of students will complete the exam in less than 40 minutes or more than 100 minutes? ﬂuisidc Srg'rom M
l,‘tct'7:,003 N 0 $70 52100
c. If you take a sample of 100 students. what is the 75" percentile sample mean (in other words.
what would be the sample mean time taken to complete the exam such that 75% of all the sample means woutd tie below it)? Sim/H 075m)
.7500 _:_ 7033707134) ((170 z? X: ?0.£a7
5+
5. Internet companies took a beating on Wall Street durinng ﬁrst four months of 2000. The
following table contains returns (in %) for a sample of the 10 largest intemet Mutual Funds for the ﬁrst four months of 2000. —— Fund Return X
Munder NetNet 24.4 — __
Goldman Internet Tollkeeper 450 a  62:)
Kinetics: Internet 321 Merrill Internet Strategies 41.0 Firsthand e—Commeroe «24.6 Amerindo Technology 41.9 Enterprise Internet ~25} RS Internet Age 24.9 ING Internet 439.9 Jacob Internet Fund 50.5 3. Compute the mean of the returns. i; '"' $90 0. If 20': 4:12 = 1075.3. compute the variance and standard deviation of the returns. 52’£%P1: 5—0735: “4.473 54033 c. if a sample of the smallest lntemet Mutual Funds has a variance that is smaller than the above
largest Intemet Mutual Funds. what would you say to your friend about how small and large
Internet Mutuat Funds compare in terms of risk and volatility? similctﬂﬁi'tbzl Funds 0.69 1655 volattlﬁ 2
+931“th less (vista 6. in 2007. the correlation between the square footage of property sold (X) and sales price (Y) for the
downtown Austin commercial district was +19. 3. Sketch an example of what the scatter plot for these data might look like. b. What percent of variation in sales price can be predicted by knowing square footage? r71 7502” .oatii c. If the correlation had been .79, what percent of variation in sales price could be predicted by
knowing square footage? Explain your answer by comparing it to your answer to part b. (pgflldlo 7 The Correlaﬁon is n tit/e; \
but the, same, $fi“£n3{h (5‘ Hang” 7. A researcher is interested in determining whether one can predict the score on 3 statistics exam
from the amount of time spent studying for the exam. He collects data from a sample of 50 students.
Each student gives the researcher the number of hours heishe studied and the researcher obtains the
test grade for each of these students from the professor. a. In this study. what is the explanatory variable? What is the response variable? ' . N
b. Assume that as a result of this study. the r r ﬁnds a correlatio tween time spent studying for the exam and score on the exam = +.91. What percent of the variation in exam score is likely to be associated with something other than time spent udying? c. Is the above study an observational study or an experiment? Explain. W‘) _
r ﬂow; #7?szth 8. A mutual fund newsletter advertises that “diversiﬁcation is an important faCtOfﬁ MW
investment success. A welldiversiﬁed portfolio includes investments whose return rates have low
correlations.‘ You review a table of correlations between return rates of various classes of
investments. You see that the correlation between municipal bonds and largecap stocks is .75. You
also notice that the correlation between municipal bonds and smallcap stocks is .2. a. if my portfolio is already heavily invested in municipal bonds. and I wish to add an investment in
accordance with the diversiﬁcation advice above. should I invest in largecap or smallcap stocks? Explainwhy Small Casi} betnurse they have low",
corralnﬂl’tarx u) mumgendg ‘ b. if I want to invest in something that will do well an my municipal bonds are not doing well. what wouldYOUsuggestilookfor? ILDOK par inqegiﬁrhgni’ whose/3
Y‘ﬂ'l'tli'ﬂ 3% negaﬁ‘vé'j MP? MJ) muv\&Idg X *5” ID 0
ng’ﬁer "‘75" ‘50 j .= as
D» 0899 M 50 :60 7. 8 .0?
12 .12
18 .25
23 .37
35 .50
42 .65
45 .75
50 .95
60 1.00 a. What is the 5number summary for those waiting times? 5, )9, 35/45, (90
b. if you get your pizza in 48 minutes what can you say about your waiting time? you. are ‘m fke H"H'I Quar‘hla 04 LLHJﬁNI‘ ‘Hn'eﬁ /
c. The middle 50% of waiting times fall between t Z and [L5 minutes. ...
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 Spring '09
 Gemberling

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