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8.1 Binomial Distribution

8.1 Binomial 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)

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8.1 Binomial Distribution

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  1. 8.1Binomial Distribution Homework Review

  2. 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

  3. 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

  4. 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

  5. 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

  6. 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

  7. 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. 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

  9. 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

  10. 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

  11. 75 85 80 Z=(85-80)/6.9282 = .7217 Normcdf (-.7217, .7217) = .5295

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