Transcript 8.1 Binomial Distribution

8.1
Binomial Distribution
Homework Review
8.4: GUESSING ON A TRUE-FALSE QUIZ
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Since True false … p = .5 … n = 50
(a) P(X  25)
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(b) P(X  30)
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= 1 - P(X < 25) = 1 - P(X  24) = 1 – binomcdf (50, .5,
24) = 0.5561
= 1 - P(X < 30) = 1 - P(X  29) = 1 – binomcdf (50, .5,
29) = 0.1013
(c) P(X  32)
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= 1 - P(X < 32) = 1 - P(X  31) = 1 – binomcdf (50, .5,
31) = 0.0325
8.6: DAD’S IN THE POKEY
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Since 2% behind bars … p = .02 … n = 100
(a) Satisfy Requirements?
F: N = 100; I: Each kid is independent; S: Each kid
has same probability of .02; T: In pokey or not
(b) P(X = 0)
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What is the probability that exactly none of the kids in the
sample of 100 will have a father in prison
P(X = 0) = binompdf(100,.02,0) = 0.1326
P(X = 1) = binompdf(100,.02,1) = 0.2707
(c) P(X  2)
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= 1 - P(X < 2) = 1 - P(X  1) = 1 – binomcdf (100, .02, 1) =
=1-[ P(X = 0) + P(X = 1)] =1 - 0.4033 = 0.5967
8.8: MARITAL STATUS
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25% of women never have been married … 10
random women are chosen
(a) n? p?
 p = .25 … n = 10
(b) P ( “ Exactly 2 ” )
 P(X = 2) = binompdf (10, .25, 2) = 0.2816
(c) P( “ 2 or fewer ” )
 P(X  2) = binomcdf (10, .25, 2) = 0.5256
8.10: BROCCOLI PLANTS
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About 5% of broccoli plants die. You purchase 10
(a) Use binomial formula to find P( “you lose at
most one of the plants”)
 P(X  1) = P(X = 0) + P(X = 1)
0.9139
8.12: GRADUATION RATES
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The number of athletes that graduate is given by
B(20, .8)
Use the binomial formula to find P( “that all 20
graduate”)
 P(X = 20) =
0.0115
Find P( “not all 20 graduate”)
 P(X < 20) = 1- P(X = 20) = 1 - 0.0115 = .9885
8.14: CORINNE’S FREE THROWS
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The number of made shots that Corrine makes is
given by B(12, .75)
Use the binomial formula to find P( “she makes
exactly 7”)
0.1032
 P(X = 7) =
8.16: HISPANIC COMMITTEE MEMBERS
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n = 15; p = .03
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(a) What is the mean number of Hispanics?
 E(X) = np = (15)(.03) = .45
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(b)
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Standard Deviation?
0.6607
(c)
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Standard Deviation? p = .1; p = .01
1.1619
0.3854
Notice that as the p-value get closer to zero, the standard deviation
also gets smaller.
8.18: MARITAL STATUS OF EMPLOYEED WOMEN
 n = 10; p = .25
 (a) What is the mean number of Employed Women?
 E(X) = np = (10)(.25) = 2.5
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(b) Standard Deviation?
1.3693
8.20: MARKET RESEARCH SURVEY
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n = 200; p = .4
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(a) Is a binomial distribution reasonable?
 F: N = 200 in survey; I: Each resident is independent; S: Same
probability of . Each time since random; T: Either seek
nutritious or not
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(b) What is the mean number and standard deviation of people
who seek nutritious food?
 E(X) = np = (200)(.4) = 80
6.9282
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(c) P(75 < X < 85) =
 Rule of thumb: np = (200)(.4) = 80; nq = (200)(.6) = 12
75
80
85
Z=(85-80)/6.9282 = .7217
Normcdf (-.7217, .7217) = .5295