Applied 40S April 17, 2009

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More on binomial distributions.

More on binomial distributions.

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  • 1. Working With Binomial Distributions or all about alarm clocks Puzzle Alarm Clock by evadedave
  • 2. How many girls are there in a family of four children. Find the probability of there being 0, 1, 2, 3, or 4 girls in the family.
  • 3. Type of Distributions... Binomial Distribution: data is discrete (# of heads when ten coins are tossed, # of spades in a 13 card hand , etc.). When a binomial experiment is conducted many, many, many times a portion of the related histogram approaches the shape of the normal curve. Probability of the number of girls in a family of four. Experimental Binomial (Probability) Theoretical Binomial Distribution (Probability) Distribution
  • 4. Theoretical Binomial (Probability) Distribution binompdf(trials, p, x [this is optional]) trials = number of trials p = P(success) x = specific outcome
  • 5. The Binomial Coin Experiment http://www.math.uah.edu/stat/applets/BinomialCoinExperiment.xhtml
  • 6. • When a manufacturer guarantees a toaster for one year, the toaster will work fine or fail in one year. The manufacturer knows that, on average, 5 percent of the toasters fail. What is the probability that the manufacturer will have to replace 120 or more toasters in a year when 2000 toasters are sold? binompdf(trials, p, x [this is optional]) trials = number of trials p = P(success) x = specific outcome
  • 7. In a 13 card hand, what is the probability of getting exactly 6 spades? In a 13 card hand, what is the probability of getting 6 or more spades?
  • 8. There are five children in a family. Assume that boys and girls are equally likely. HOMEWORK 1. What is the probability that three are girls? 2. What is the probability that there are at most three girls (i.e., there may be 0, 1, 2, or 3 girls)? 3. What is the probability that there are more than two girls?
  • 9. A shipment of 200 tires from a tire manufacturing company is known to include 40 defective tires. Five tires are selected at random, and each tire is replaced before the next tire is selected. (a) What is the probability of getting at most 2 defective tires? HOMEWORK (b) What is the probability of getting at least 1 defective tire? (c) What is the probability of getting 2 or 3 defective tires?
  • 10. At a certain hospital, the probability that a newborn is a boy is 0.47. What is the probability that between 45 and 60 (inclusive) of the next 100 babies will be boys? HOMEWORK