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**Unformatted text preview: **STS 2610: Quantitative Methods Spring 2014 JQHWAM 21 lUl‘i’ More on the Standard Deviation ifr r Example: Dr. Kramer gives weekly quizzes (10 questions, 5 points each, no partial credit) in his
probability class. The score distribution for last week's quiz is given below. sampir dmanm =
31 ._ 20(st
h‘l F a. Calculate the median quiz score. - ram.“ [ha-“3%! ' 53-5 (W a; 53‘“) WOMN’ 40 mOdf‘ 40 b. Calculate the mean quiz score. y M‘ 25 ”“5" '1 '35 23 . +052 445 m .50: a319,:
“4 ’7‘ c. Calculate the standard deviation of the quiz scoresa 5‘»-~ 0.1 c it)“ 1 0.13154193002 sﬁgﬁ-élﬁ’ﬂ) . . (510-5? (31(3)
N H}
. . . e 1 : -. > ‘
W O" 5.723;“: 4533 7 : Q‘VO Wells Fargo Banks call center has representatives that can speak English and Spanish. The lengths
(seconds) of a sample of 11 calls in which English was spoken are given below along with the lengths of
14 calls conducted in Spanish. mmmmmnnmmmm
mnmm 151 127 147 mammalian-alg- Engiish: mean = Y ' 1H3? standard deviation = 5'- 2141
Spanish: mean = 1 2 ISO at standard deviation = 3= 20 .‘ﬂ Which group has the more variable call lengths? Spamlh ' in iaiqcrsiandard
dcm’ahm (mb'lrt' van'ahm) Fiﬁ [Mint van‘a mm”? 7‘ :
22.42 W i
coefﬁcient ofvariation - CV1 3-75-(IM) CV: " I”. 3.? (‘0‘) ‘ 80 3%]. Li Gamma) dt’v C\i=,%:Uw) CV3: 2".”rLIw): new]. E -/, 0‘ man Thm S10Hd01d 150.81: . J vanah‘cn it’laM
0040116" '5 7’ mifai‘ﬁf‘ man Exercise: Data for samples from muiti-vitamin tablets from two manufacturers are given below. Prescott Pharmaceuticals Vitacorp
500 mg 250 mg
n = 100 n=200 .
i=500.02 i=249.03 Nana (V
s=10.3 s=7.9
'\ 7‘ lw variation,
mm conststm’t Which manufacturer appears to have a more consistent manufactﬁ'ing process? - l.5 . _ ' q. ’ . ~.\
0’? 3%551 (HID ‘ 1'0“" CV; 21509050“ LajPCC/
man—“Man
X-Y
. - , any
Jig- Wmmrmrni—mmn 2: x ‘5? it‘lls hiwm
(Siamlaidrirdvalut) (1“,.qu swam a 5 -» Standard dt‘v abovc
. Imam 2 :m or bclow am a
*WWW 0‘ mraswcmmi ans .v... cmpi'tffou Ruif { i More Information from the Standard Deviation: 17/.” 2‘7,
, Emp'nca' Rule ' J I i N“ A4.— Afar “'5" N» K" H316 N"
1- “PPM 08/. 04 mt’wmcmrm at dasin'ommn
fan WW“ ' Simdaid dz‘wanm ct 1hr mm C“) (A. (MU?)
2-099“ “‘5"- 0" mrmmcmmu win tan
“4'" Z “Gilda“! dmahm a mm” (m 20’. Any) 3. 7.
max-M71. ‘ 35iandaid dm‘am (ﬁx-3r 11'5““) "scar“ , _; a” a 5115* use we \“"V'll
515- @440 Example: 9 us a. 56 w 7“
0 Suppose that the distribution of SAT math scores for last year was approximatelng with W33"
score u z 515 and standard deviation 0 s 115. — M What proportion of scores fall between 285 and 745? 0m Whatproport‘iotnnotﬁorfssfilajogizﬁoi : l i 33' ”(~0ny “Wk 5
2. '2— __/ a What proportion of scores fall below 285? a 51' Egg; 5/1.: 2151-5 5 5,
. ‘ '(b’q 2" '. a. I ‘
Whatproportionof scores fall between {3553 “3’02 "'1’ 7.
3+1. $235.... What proportion of scores falquetween 630 and 745? . 415 \
Eli-"Asqoga'g'
” ;~ raise-51%.:,-i-;:~'--".-‘.'i 7“ ' a
i
:1:
4'
9
E“.
‘. ~— %ﬂf’———m ' ' ii at
5M2!“ ' 9;. 145 . WW K smndmd dwahm “mm"
iguana mm matrix at mcaswrmcmi “NM m“ l- i1 ' to! 5 mm
2' (lob-Liz 75/. -0H(aiH$"-'"15d' a. mi - w mum 1“ “d . - . {an
4. (My at rrm» (HI
Milt {n 4: Siahda'd
mom“ . .. . . . .
[w x W: Suppose that tuition and fees at colleges and universities in the US. follow a distribution
/
‘00 with ma u = $16,500 and standard deviation 0 = $10,000.
a—I”. "' ‘
At least 15 96 of US. colleges and universities have tuitionsmuhan $36,500. ( 0: 59'5’3 I *6‘ A: most 96 of US. colleges and universities have tuitions W 546500? 5:: “.93
759,500 ”0'”- ngl’ m 50.5% - M00" (1
“J l “(f
"(3" “0’ 3 mum «A, 33 m- ...

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