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Sections 5.4 %26 5.5 Lecture Problems (1)

# Sections 5.4 %26 5.5 Lecture Problems (1) - Solutions for...

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Solutions for Lecture Problems from Chapter 5 34. What kind of problem is this? What kind of problem is this? Your choices are either binomial or Poisson. People aged 25 and older either have completed four years of college or not. One or the other, can’t be both, and no third choice. So this is success vs. failure problem. For all parts of this problem, the “success” is selecting an individual who have completed four years of college. (Looking at what is asked in the questions.) So this is a binomial problem. Let X be the r.v. that counts the number of individuals who have completed four years of college in a sample of 15 people. Given: p = 0.28, because 28% of all people aged 25 and older have completed four years of college (from first sentence of paragraph). Binomial with p = 0.28; n and x are given in the questions. (Note if p = 0.28, then 1 – p = 1 – 0.28 = 0.72) Then Prob ( X = x | n , p ) is calculated by ( ) ( ) x x . . ! x ! x ! . p , n | x prob - 5 - 5 1 72 0 × 28 0 × 1 15 = 28 0 = 15 = a. Want Prob ( x =4 | n =15, p =0.28). Chap 5 lecture problems 1 © Harvey Singer 2009 ( ) ( ) 22616335 0 = 026956 0 00614656 0 1365 = 72 0 × 28 0 × 13 × 7 × 15 = 72 0 × 28 0 × 1 × × 11 × 1 × 2 × 3 × 4 1 × × 11 × 12 × 13 × 14 × 15 = 72 0 × 28 0 × 11 4 15 = 72 0 × 28 0 × 1 4 15 = 28 0 = 15 = 4 = 11 4 11 2 11 4 4 15 4 . ... . × . × . . . . ... ... . . ! ! ! . . ! ! ! . p , n | x prob - 4 - 5

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So Prob ( x =2 | n =6, p =0.23) = 0.2262. b. Want Prob ( x ≥3 | n =15, p =0.28). Prob ( x ≥3 | n =15, p =0.28) = Prob ( x =3 | n =15, p =0.28) + Prob ( x =4 | n =15, p =0.28) + Prob ( x =5 | n =15, p =0.28) + … More clever way is to use complements. Prob ( x ≥3 | n =15, p =0.28) = 1 – [ Prob ( x =0 | n =15, p =0.28) + Prob ( x =1 | n =15, p =0.28) + Prob ( x =2 | n =15, p =0.28)] Prob ( x =0 | n =15, p =0.28) = 0.0072 Prob ( x =1 | n =15, p =0.28) = 0.0423 0 15 15! (0) (.28) (1 .28) .0072 0!(15)! f = - = Prob ( x =2 | n =15, p =0.28) = 0.1150 Prob ( x ≥3 | n =15, p =0.28) = 1 – [0.0072 + 0.0423 + 0.1150] = 1 – [0.0072 + 0.0423 + 0.1150] = 1 – 0.1645 = 0.8355 Chap 5 lecture problems 2 © Harvey Singer 2009
35. What kind of problem is this? What kind of problem is this? Your choices are either binomial or Poisson. Students either withdraw from the course without completing the course or not. One or the other, can’t be both, and no third choice. So this is success vs. failure problem. For all parts of this problem, the “success” is selecting an individual who has withdrawn from the course. (Looking at what is asked in the questions.) So this is a binomial problem. Let X be the r.v. that counts the number of individuals who have withdrawn from the course in a sample of 20 students. Given:

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Sections 5.4 %26 5.5 Lecture Problems (1) - Solutions for...

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