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**Unformatted text preview: **"1,; . :::: O) 4 37. Comd'aiém 6M . '3. From pas? experience, a company has found The? in carions of Transistors, 92% coniain no defecﬁva Transisiars; 3% coniain Two defective Transisfors, and 2% canmin Three defeci’ive fransisfors. ;g' 2 1:141 511% deémi'iwiﬁ 11éiiw-mxg [-87% (Em-S - - ~
a. What is fhe expec’red number of defective Transisfors? ‘ 11.1 id (1131101) a C a 33-21“ :13? ‘3?)
:0%‘iﬂ{5§+ 6‘574.
, ., . .i i . 1 firs is
E3. Calcuia'i‘e The variance and sfandar-d deviation. m 1‘ ‘ O 151
o’xzqrbbw“5‘310‘42311651.ISE—Ligwi‘}"if: 21—13")? 3)* (3~ ! 5") ( 03:) : oooa0¥+ Qaﬂlél"€1;3+0u103\;’ 1:11 Oaitoéij m @T:ZEE> M...__...____M __ N A” "W .1 "L
57“ t: ( 0'33?“ "1,301‘Q: 1&5 (6—7” at. Aboui how many exim Transisfor‘s per day would "the company need to repiace The defecﬁve ones if if used 10 car'igns per day?
3106553) '2" i_.05’
FWﬁkmékfg 1. The number of sui’rs said per day at a remil s‘rore is shown in The iabie wiih “the. correqunding probabiii‘i’ies.
$ng Number- bf sui‘rs said, X 19 20 21 22 23 Probabilities P00 0.2 0.2 0.3 0.2 0.1 a. What is fhe expec:ed number of Sui‘i's said per day?
/!/L D! - ﬁx”? .'-; ifii if. 3%} +1 ENG {1 12:3 ,3, “5:13 5; EX 4'” “3‘2” 5. E } «if 42- iii 4- i) n M\. , . I
s. .1 I; V v”
11‘! Li} 7 VT 5; u I + :3 W b. If ‘rhe manager of The retail Siore wanfs To be sure The? he has enough suii‘s far ‘ihe next
5 days, how many shouid the manager purchase? ' ”HAM Mp1 a, ~1- m.“ “A,” Sgoi, Gad ad}? 1 '2. A io‘riery offers one $1000, one $500 prize, and five $100 prizes. One Thousand Tickets are
said a? $3 each. Whaf is your average payoff for one Ticker? How much does fhe loh‘ery
' "keep from each iicke’r in ihe iong run? \ i; “ax .- 5 "a 2 3' {’62 '2‘ " i
W" m s i z" .- . ' -'n "’" -"‘ 2.7 it". w 1""! —._. " *' . n;
h \Oaﬂ (ifiaci03“§"1£3“5 2[:€:}.:Jis)2% intuié‘ﬁ {40539} ‘2‘" “1 iiii‘i
._ w t , k,- .. in (Q 5:, averzikfgli “Pei? mtg
\ m La #2223 Erie {:2 f5; 2% i i
3. The probabiiiiy disiribu‘rion shown-represents fhe number of Trips of five nighfs or more fha’r
American aduiis Take per year. (Thai is, 6% do no’r fake any frips [asfing five nights or more,
70% fake one frip iasii‘ng five nighis or more per year, 20% fake two Trip ias‘ring five nighi’s
or more per year, [email protected]% Take ﬂiree Trip lasting five nighi‘s or more per year, and 1&3 Take four
irip iasfing five nighfs or more peryear. a. What is fine expecied number of irips iasiing five nigh’rs or more per year Taken by
American aduiis? 2 6? i222 sis 2i 2s [.22 is i. i is 2» I “i ‘ii
’ GIN ”it"!
b. Caicula’re 'i'he variance and standard deviai'iim. 7;; . :3. (O "’"' ‘rvzg>wnfjﬁéﬁ>“} {)3 ﬂgiag‘itflﬂ) +61%? “5r&5>a(l aria-”B ”j“
i K a“ f
C3“? 2,2210 wifwws} {O Ks Sfaﬁsﬁcs Name:
Random Variables Review Date: Period: 0 1. Give. two exampies of discrefe and coaﬁnuous varéables. D35¢rg+e ' ‘35 D4? £49éas—VEE‘; in 6*. ﬂﬂkﬁ S
W’ a? [4‘5 on a.» $354” £¢n+fmumaa °' Tempe FOAUWZU Hedcyﬁ" “a as shown. This is an exam 16: of a probability distribu‘rion. ,
Number of fies, X 4 Probabili'ry, [’00 0.30 0.5 a 1 0.08 0.02 a. Construc? a hisfogr'am of i'hjgz probabiﬁ’ry disfr‘ibu‘rion. 4322.3"! b. Find The foilowing probabiliﬁeswfzhow what decimals you added or‘ sub’rmcfed. 1. Find The probabiii'ry Tha‘r a cusfomer- wilt buy more Than 1 Tie.
90 >1\ = .\ was? «9?- ﬁ 62 2. Find The probabilify That a cusfomer wiEE buy 3 or less ﬁes.
PC¥ E 3:): ,3+. 5+” 2+ .og: .Cc‘a’, . 3. 130(22): .t+.og+.c?—zam
4. P(X:2)= A 3. A uniform densi’ry curve is constant between 0 and 4, and O eisewhera. Sketch The curve. \ eru.)
M a. What is The heighf of The. density curve?
\/'-ﬁ
E). Find P(X : 2.65) = o ' c. FindP(X>2_3)= (LPZJQC/‘h: ‘3 cf. FindP(2.1;g><53,5)= methﬁVQ: ."sa: 2. A? Tyler‘s Tie Shop, Tyier found ’rhe probabitiﬁes The}? a cusfomer will buy 0, 1, 2,3, or 4 ﬁes, 23:? 4. Skefch The normal curve and Show oli your calcuiaﬁons. The average waiting Times To be seated for dinner of a popuiar resiauranf is 23.5 minufes, ‘
wifh a sfandard deviaiion of 3.6 minufes. Assume The variable is normaliy disfribui‘ed. When
a pofron arrives at ”(he resiauroni for dinner, find the probobiiii‘y The? fhe pofron wit! have To wait The following Time. ‘ x w? M {5995 .3“, 3' ‘93
a. Befween 15 and 22 minuies.
is“ tee“ a: 31“” 5'
'23» W
ng‘t‘g
.2: 7. ~— Ra 310i] 7% 1. _. normm\aé~9 (:2. 3k)“ J W» b. 20 minu‘ies or more.
'3 1 2.0 r 23 AS’ 3.6:: 5f», “0.9%21 {“3 ”3.3bH #351. «25 we «was i .. 3, M R
marmoioée‘;(miﬁﬁigrﬂi’ﬂmb:(96’3 Gail) 5. A chemical supply company currenfiy has in stock 100 Eb of a eerioin chemicoi, which if sells To
cusi'omers in 5—Eb iofs. Le? X = The number of iofs ordered by a randomiy chosen customer. The urobc'ibili disfribuﬁon of x is shown in ”the char? below.
3
.3 a. When“ is fhe expected number of iofs ordered by a cusiomer? ﬁx: é xifj’i 3: 3623 aw 261%»? $6334” hiﬂJ) ng 2° (:2: 3
QUWomgﬁﬁ; I<l $0 b. If The manager of The store won‘rs To be sure The? he has enough iois far The max? 5 '
“5 how many shouid The. manager have on hand? g€g5§3 2 ms” A+ leoo'ir i&,_ me he toga» an?“ 4kg. ekerr'xiﬂtodi. 6 A box containing Ten $1bilis,five $2 biils Three $5 bills one $10 bili and one $100 bilt A
person charged $20 To selec’r one bit! a. Consirucf a probabéiify disiribufion of The payoff amount X. 1?? b. Whiz? is The expec’red payoff for one ﬁche? if “the icing run?
;1'( Au?) 4— 2( FAQ) +§(”/3o+ WQ(/éa>*ioo{/§o) 3'» $.31? wwéﬁfa 1 u‘I\\ keep 5 3”}? In 4&4" \Iznq‘ wwh ‘
W c. How much'does The house expeci’w‘ro keep from each be? in The long run? 2:» w $23": #2; 3—57 . {(5% bend ti“, w,‘// A??? ﬁ/QeFS’. d. Calcula’re the sfandard deviqﬁon of 1rhea distribu’rion Show aii work including The formula
and how you plugged The numbers m. OVK :2 ‘1 éi€fé "Mm :gjm
{aw ;.3§:f(>"3+ (2,3,15§1('2§3 * (9%2’3516WB” ('0'?'2552['5f>+€°oﬂm57© 7' 1 H5?.u%9-5§" "$933k: v ...

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