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Binomial vs. Geometric

Binomial vs. Geometric. Chapter 8 Binomial and Geometric Distributions You have 5 minutes to study for the Chapter 8.1 Reading Quiz. HW for Tues/Wed. Chapter 8 Read/Notes: section 8.2 Do: #8.37, 45, 50 Reading Quiz Jan 12 th or 13th (No Notes) Focus on:

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Binomial vs. Geometric

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  1. Binomial vs. Geometric Chapter 8 Binomial and Geometric Distributions You have 5 minutes to study for the Chapter 8.1 Reading Quiz

  2. HW for Tues/Wed. • Chapter 8 • Read/Notes: section 8.2 • Do: #8.37, 45, 50 • Reading Quiz Jan 12th or 13th (No Notes) • Focus on: • Requirements of Geometric Setting (4) compared to Binomial • Formula for Geometric Probability and P(x>n) • Formula for finding the mean and standard deviation of Geometric Distribution

  3. Are Random Variables and Binomial Distributions Linked? Suppose that each of three randomly selected customers purchasing a hot tub at a certain store chooses either an electric (E) or a gas (G) model. Assume that these customers make their choices independently of one another and that 40% of all customers select an electric model. The number among the three customers who purchase an electric hot tub is a random variable. What is the probability distribution?

  4. Are Random Variables and Binomial Distributions Linked? X = number of people who purchase electric hot tub X 0 1 2 3 .288 P(X) .216 .432 .064 (.6)(.6)(.6) GGG EEG GEE EGE (.4)(.4)(.6) (.6)(.4)(.4) (.4)(.6)(.4) EGG GEG GGE (.4)(.6)(.6) (.6)(.4)(.6) (.6)(.6)(.4) EEE (.4)(.4)(.4)

  5. Combinations Formula: Practice:

  6. Developing the Formula Ex. 8.1 Blood Type; pg. 440 – Pract. Of Stats 2nd Ed Blood type is inherited. If both parents carry genes for the O and A blood types, each child has a probability 0.25 of getting two O genes, thus having blood type O. Let X = the number of O blood types among 3 children. Different children inherit genes independently of each other. Since X has the binomial distribution with n = 3 and p = 0.25. We say that X is B(3, 0.25)

  7. Developing the Formula Outcomes Probability Rewritten OcOcOc OOcOc OcOOc OcOcO OOOc OOcO OcOO OOO

  8. Developing the Formula Be able to recognize the formula even though you can set up a Prob. Distribution without it. Rewritten n = # of observations p = probablity of success k = given value of variable

  9. Working with probability distributions State the distribution to be used State important numbers Binomial: n & p Geometric: p Define the variable Write proper probability notation

  10. Twenty-five percent of the customers entering a grocery store between 5 p.m. and 7 p.m. use an express checkout. Consider five randomly selected customers, and let X denote the number among the five who use the express checkout. binomial n = 5 p = .25 X = # of people use express

  11. What is the probability that two used the express checkout? Get started by checking required components: 1. Are there 2 categories? What are they? 2. Is the probability of a success the same in each trial? What is it? 3. Are the trials independent? 4. Is there a fixed number of trials? How many? • Binomial, n = 5, p = .25 • X = # of people use express • P(X = 2)

  12. Calculator option #1:nCr = n choose r = 5 math prb #3: nCr 2 enter 10 REQUIRED COMPONENTS 1, 2, 3 • Define the situation: Binomial, with n = 5 and p = 0.25 • Identify X: let X = # of people use express • Write proper probability notation that the • question is asking: P( X = 2) Calculator option #2: 2ndvars 0:binompdf(5, 0.25, 2) = .2637

  13. What is the probability that no more than three used express checkout? • Binomial, n = 5, p = .25 • X = # of people use express • P(X ≤3) P(X ≤3)=P(X=0)+P(X=1)+P(X=2)+P(X=3) Calculator option: P(X ≤3)= binomcdf(5, 0.25, 3) = .9844

  14. What is the probability that at least four used express checkout? • Binomial, n = 5, p = .25 • X = # of people use express • P(X ≥ 4) Calculator option: P(X 4) = 1-P(X<4) 1-binomcdf(5, 0.25, 3) = .0156

  15. “Do you believe your children will have a higher standard of living than you have?” This question was asked to a national sample of American adults with children in a Time/CNN poll (1/29,96). Assume that the true percentage of all American adults who believe their children will have a higher standard of living is .60. Let X represent the number who believe their children will have a higher standard of livingfrom a random sample of 8 American adults. binomial n = 8 p = .60 X = # of people who believe…

  16. Interpret P(X = 3) and find the numerical answer. binomial n = 8 p = .60 X = # of people who believe The probability that 3 of the people from the random sample of 8 believe their children will have a higher standard of living.

  17. Interpret P(X = 3) and find the numerical answer. binomial n = 8 p = .60 X = # of people who believe P(X=3) = binomialpdf(8, .6, 3) = .1239 or

  18. Find the probability that none of the parents believe their children will have a higher standard. • binomial, n = 8, p = 0.60 • X = # of people who believe • P(X = 0 )

  19. Find the probability that none of the parents believe their children will have a higher standard. binomial n = 8 p = .60 X = # of people who believe or P(X=0) = binomialpdf(8, .6, 0) = .00066

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