8.1Binomial Distribution

Homework Review

8.4: GUESSING ON A TRUE-FALSE QUIZ

Since True false … p = .5 … n = 50 (a) P(X 25)

= 1 - P(X < 25) = 1 - P(X 24) = 1 – binomcdf (50, .5, 24) = 0.5561

(b) P(X 30) = 1 - P(X < 30) = 1 - P(X 29) = 1 – binomcdf

(50, .5, 29) = 0.1013 (c) P(X 32)

= 1 - P(X < 32) = 1 - P(X 31) = 1 – binomcdf (50, .5, 31) = 0.0325

8.6: DAD’S IN THE POKEY 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)

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) = 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

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

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

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) =

Find P( “not all 20 graduate”) P(X < 20) = 1- P(X = 20) =

0.0115

1 - 0.0115 = .9885

8.14: CORINNE’S FREE THROWS

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”) P(X = 7) = 0.1032

8.16: HISPANIC COMMITTEE MEMBERS n = 15; p = .03 (a) What is the mean number of Hispanics?

E(X) = np = (15)(.03) = .45

(b) Standard Deviation?

(c) Standard Deviation? p = .1; p = .01

Notice that as the p-value get closer to zero, the standard deviation also gets smaller.

0.6607

1.1619

0.3854

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

(b) Standard Deviation?1.3693

8.20: MARKET RESEARCH SURVEY n = 200; p = .4 (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

(b) What is the mean number and standard deviation of people who seek nutritious food? E(X) = np = (200)(.4) = 80

(c) P(75 < X < 85) = Rule of thumb: np = (200)(.4) = 80; nq = (200)(.6) = 12

6.9282

Z=(85-80)/6.9282 = .7217

Normcdf (-.7217, .7217) = .5295

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