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Unformatted text preview: ID: ____________________________ Quiz section or time: ____________________________ —7+ﬁ Stat/Math 390, Winter, Test 1, Jan. 23, 2009; Marzban
Open everything, closed messaging/ discussion
Check front page and back page.
Multiplechoice: mark answers on these pages. DO NOT EXPLAIN.
The rest: SHOW your answer and your WORK, on these pages;
Points NO CREDIT FOR CORRECT ANSWER WITHOUT EXPLANATION. 1 L1)? 1. Suppose the grade that separates the top 75% of all grades in a class is 25.
a) Then a grade of 25 is the 75th percentile of grades. @Then a grade of 25 is the 25th percentile of grades. L7 5
c) Then a grade of 75 is the 25th percentile of grades. > ’X
d) Then a grade of 75 is the 75th percentile of grades. 25‘
e) none of the above. [’4’ W LG. 1 VII
2 ‘3 2. at 1 in 200 people carry a certain defective gene. Let x denote the number of
people carrying this gene in a population of 1000. Then, the distiibution of x is approximately Poisson. Which of the following can be estimated from that distribution?
a) The proportion of people carrying this gene. b) The proportion of people carrying this gene, in a population of size 1000.
c The proportion of all populations, with 1 carrier of this gene. @The\9 piop01tion of all populations of size 1000, with 1 carrier of this gene. \/
lLl L?“ s is the standaid deviation of a bunch of length measu1ements 1n mete1s. The standaid
C_ LQQ deviation of those same numbe1s measu1ed 1n centimete1 i
a b) 105 1,01) )5/100 5272145 5= lehilcx'“) ﬂows :7 Sues ssuming x has a n01 mal distiibution, then one can estimate its mean and standaid deviation, om inf01mation contained in
.boxplot b) a pe1centile c) median and mode d) none of the above .\’> 2371VC¢W1L¢J :7 1441/1. 2. WALmIs (‘01 gAbxﬁﬂ +55+2 Consider w iAiting onto a computer disk and then sending it through a certi r that counts the
be1 of missing pulses on one disc Suppose this numbe1 has a Poisson distiibution with A— — 0. 2.
lf the disks a1e giouped ten to a package, the total numbe1 of missing pulses on all ten discs will have a Poisson distiibution, as well.
a) Without much (or any) calculation, give one 1eason why the pa1amete1 of this latter Poisson distribution is given by A 2 10(0. 2) = 2. x; 4‘: b4 ”(ﬁrm2 PJY'CS. A: area" ml. /‘l' {VILJ/ MI ’X 1 u 61's 0.2 1w 1 Am, ,+ “4111“ 2 w to cum.
b) What proportion of packages will have at least two missing pulses on the discs in the package?
You may use Table 111 if you wish. Give a numerical answer, but show work.
2 YlX:1)+Y(K:3)+—LH PWUZZI : l— ﬁlmybcol +Y¢oy(x=l)} oz 21—1943? J. o 7.11): [0 5%} 2 QJM 6. A repairman assesses a ﬁxed Charge of $10, plus $20 an hour that he spends on a job. Then the revenue resulting from a job that takes x hours is 10 + 20x. Suppose he knows the density function
for x is ﬁx). What is the Expected Value of his revenue, if the Expected Value of x is 5 hours.
Note: The Expected Value of a function of x, e.g., g($) = 10 + 20x, is deﬁned as fg(x)f(x) dx.
Show work; Don’t just give an intuitive answer! EEKO—kﬁLOx] {— f(ro+zox) fo) 01x —— to {in} dx 1 9.0 577678”) cl! 5”) \/—/—D
1 EE¥1=§ 2 @istorical data implies that 20% of all components of a certain type need service while under
arranty. Suppose that whether any particular component needs warranty service is independent of whether any other component does. lf these components are shipped in batches of 25, Ebﬂd x denotes the number of components in a batch that need warranty service, determine the long—run
proportion of batches for which the number of components in each batch that need warranty service strictly exceeds the mean number by more than 2 standard deviations. You may use the Binomial
Table 11 in the back of the book. Give a numerical answer, but show work. Foxf lolwomtrve [1:va “ 23(IQ) : 5— V=an(t—w) = Janna) = 2 \3«3?Lx>/\4+Qo) : ?YDY(X>Ol) — 0.0\\+ 0.00% + 0.001 _,. a~~~ —. lam—+3 /
2( Ila'3 8.>Let EM denote the Expected Value (or mean) of a discrete variable x with a mass function
p(x). Show that the variance of x can be computed as E[x2] — (E[x])2, where E[x2] = Zx2p(x). \ILx—S : é, (x— EExBY—Ptx) 3—,; ¥ 7 1
EExlj EE‘) 1. : EExll — (EDQYL. : 2 x19“) _ a EH31 x PM) waxy; 1W) ...
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