10/1/2012

Complete Chapter 4

• Approximating Binomial Probabilities
  • Normal Approximation
    • Suppose 35% of the TV viewers in a metropolitan area are watching a certain program. Find the probability that in a random sample of 1,000 TV viewers, at most 330 are found to be watching the program.
  • Justification for Poisson Approximation
• Poisson R.V.
  • Consider a continuous time process with the following characteristics:
    • The probability of a given number of events in an interval of size t doesn't depend on its location.
    • Events in intervals that don't overlap are independent.
    • The possibility of more than one event in a small interval can be neglected.
    • In a small region, the probability of occurrence of an event is approximately proportional to the size of the interval.
  • A process with these characteristics is called a Poisson process.
• Hypergeometric Distributions
  • A company receives a shipment of 20 items.  Because inspection of each individual item is expensive, it has a policy of checking a random sample of 6 items from such a shipment and accepting delivery if no more than one selected item is defective.  What is the probability that a shipment with 5 defectives will be accepted?
    
• Approximating Hypergeometric Probabilities with the Binomial Distribution
  • Suppose that 10,000 individuals (4,500 women and 5,500 men) attend a sporting event.  Five ticket stubs are drawn at random, without relacement, to receive prizes.  Find the exact probability that three men and two women receive the prizes.  Use the binomial distribution to approximate the probability of interest and compare your answers.
• Group Exercises

Please read Sections 5.1 and 5.2 for class on Wednesday.