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Unformatted text preview: . p  V :inomcdf — Practice Activity STA2023  Chapter 17
The Normal Approximation to the Binomial and the Bino u According to the U.S. Census Bureau, in 2003 about 27% of United States residents who are older than
25 years old had earned at least a bachelor’s degree. Suppose you collect a random sample of 820
residents of the U.S. over the age of 25, asking each whether or not they have a bachelor’s degree. Note that there are only twb possible answers to the question, bachelor’s degree or not. Thus each trial
has only. two possible outcomes. Furthermore, there are a ﬁxed number of trials (11 = 820), and the
probability of success remains constant from trial to trial (p a 0.27). Finally, since the data is from a
random sample and the sample is less than 10% of the entire population (all U.S. residents over the age
of 25), it’s reasonable to conclude that individual responses are independent of each other. . Thus, this scenario can be modeled with a Binomial distribution: X ~ B(820, 0.27)
' where a success is deﬁned as a U.S. resident over age 25 who has a bachelor’s degree A. Use the normal approximation to the binomial (NAB) to calculate the probability that, in any random
7  size n=820, you would ﬁnd more than 250 with a bachelor’s degree. In other words, ﬁnd
I ketch a welllabeled and shaded Normal curve and show all work. formulas can be found'in t
standardize the Normal curve to
desired probability. The desired pro {Xmas,4! $l= '09‘Suuﬁs‘3
VEXFacic/ it: m??at\ures = n f; ~.= RA»? ' ox on page 437 of your book. After calculating those values, you need to
tande Normal curve (ZCurve) so you can use the Z—Table to ﬁnd the
'lity is the shaded area under the Normal curve. "= :1 519. l. 80% are, martVa an laJ $5?S’.Ca So irks MAE will W1:
."* MM°“ALK7:QELOJ+E =22'oIr 0.2.7 ' ' Ant??? x,j«
=22/ﬂ : VI/ Edie’57“
0.9
. gen—aziff
.: 4‘. v ;
(9; Pt; x 5% Z rams: I gﬁbk a, :2? +0.73"
=/a.7/3 1' it From aiming  P(z:.=z.=e§ = 0. H79 B. According to the 68959937 rule, what percent of the time'should we expect to ﬁnd between 196
and 247 U.S. adults over 25 with a bachelor’s degree in any random sample of size n = 820? In
other words, if many random samples of size n =. 820 are collected, what percent of those samples Will have between 196 and 247 successes? x N. N ( 22 L4,!) / 97.7) _C. Use an appropriate function of your calculator (binompdf or binomcdf) to ﬁnd the true probability
that, in a random sample of 820 US. adults over age 25, we would ﬁnd more than 250 with a bachelor’s degree. Z P > g? 5‘9 Note: if a question like this is asked on the exam (in' a show all work format), you will need to write
down which function you used as well as which inputs you typed into that function (along with the
ﬁnal answer). See the answer key for what is expected of you. U5 (“3 We.  F()(>2.s9 =— \ —?O< .4. 25¢) ‘3‘” aumshm‘m'gw' f: \ JDMDMMM (sac, 0.212ch ' ’ v  as a
= 1"“ a"? 9:5,3 9&6: tn 3"? \ aux )
. :1 0.13117 ' cum ?§‘r‘ (Eark & \ 3055;32:1b‘zcimd'160 D. Use an appropriate function of your calcu df or binomcdf) to f d the probability that, a random sample of 820 US. adults over age 25, we would ﬁnd at least 230 with a bachelor’s
degree‘ , . <_‘—'.t7(x>_23o) Note: if a question like this, is asked on the exam (in a show all work format), you will need to write
down which function you used as well as which inputs you typed into that function (along with the ﬁnal ansWer). See the answer key for what is expected of you. c ' I name1")"
Wm a LDM? ‘3 POO2.239 =—. \——\>(><£.=mv A—— 54*“ we  l,— bﬂnomccﬂ‘g (320.; 6'37) 22?) \_ 0.73 9’ I . ‘ E. Use an appropriate function of‘yi‘nompdf or binomcdf) to ﬁnd the probability that, in
a random sample of 820 US. adults over age 25, we would ﬁnd exactly 260 with a bachelor’s degree.  _ K. QéKD Note: if a question like this is asked on the exam (in a show all work format), you will need to write
down which function you used as well as which inputs you typed into that function (along with the
ﬁnal answer). See the answer key for what is expected of you.  .._.i
H‘ a random sample of 820 U.S. adults over age 25, we would ﬁnd fewer than 200 with a bachelor’s
degree. /’"*‘ ‘
‘ P( x < a o <9
Note: if a question like this is asked on the exam (in a show all work format), you will need to write
down which function you used as well as which inputs you typed into that function (along with the ﬁnal answer). See the answer key for what is expected of you. ‘ , I \Gmgﬁ‘l‘f ?(X<2¢9539F(X£\99)I. Av " a
t" biﬂ'bMaof?(?M/ 3.97“, { 79 Pa.» .——..‘
_— ...
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 Spring '08
 Ripol
 Statistics, Normal Distribution, Probability theory, Binomial distribution

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