Statistics 270 - Lecture 17

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Statistics 270 - Lecture 17
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• Have covered sections 4.1-4.4
• We will NOT be covering 4.5 and 4.6though they
  make very enjoyable bedtime reading
• Today Examples from Chapter 4
• Will begin Chapter 5 next day

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Example

• Let X be the random variable denoting the time
  between successive arrivals at the drive-up
  window at a local McDonalds
• If X has an exponential distribution with l1
• Find the expected times between arrivals
• Find the probability that the time between
  successive arrivals is between 2 and 5 minutes

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Example (good test question)

• Suppose the diameter of a certain variety of tree
  (full grown) is normally distributed with mean of
  8 inches and standard deviation of 3 inches
• What is the probability that a randomly selected
  full grown tree will have a diameter between 9
  and 10 inches?
• If two trees are randomly selected, what is the
  probability that at least one has a diameter
  exceeding 9 inches?

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Example

• The amount of peanut butter in a jar follows a
  N(m, s2) distribution
• Over a long period of time that 97.5 of jars
  have a volume of 503.92ml or less
• Over a long period of time that 15.15 of jars
  have a volume of more than 502.06ml
• What are the mean and standard deviation of the
  above normal distribution for jars of peanut
  butter

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Example

• An ecologist wishes to mark off a circular
  sampling region having a radius of 10m
• The radius of the resulting region is actually a
  random variable with pdf
• What is the expected area of the resulting
  circular region