Approximating a Binomial Distribution with a Normal Distribution

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Approximating a Binomial Distribution with a
Normal Distribution
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Binomial Distribution

• Discrete- success or failure
• X number of successes
• Pproportion of Successes
• Meannp
• Variance npq

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When to Use the Normal to Approximate the
Binomial Distribution

• When your sample sizegt1000
• When binomial tables can not handle your sample
  sizes

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Continuity Correction

• To convert a binomial (discrete) distribution to
  a normal (continuous distribution), you must use
  the correction for continuity which is

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Examples of Using the Continuity Correction

• If your binomial question reads
• Then the conversion to a continuous would read

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Examples continued

• If your binomial question reads
• Then the conversion to a continuous would read

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Examples continued

• If your binomial question reads
• Then the conversion to a continuous would read

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Using a Normal to Approximate a Binomial

• Determine n and p for the binomial
• Calculate the interval,
• If the interval lies in the range of 0 to n,
  then the normal will provide a good approximation
  to the binomial.

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For example 5.54, page 248

• If n 100 and p.01, can the normal distribution
  be used to approximate this binomial distribution
• No, because the result does not lie between 0 and
  100

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For example 5.54, page 248

• If n 20 and p.6, can the normal distribution be
  used to approximate this binomial distribution
• Yes, because the result does lie between 0 and
  20

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Using the Normal to Approximate the Binomial
5.60, page 248

• 22 of all births in the US occur by Caesarian
  section ( p .22). In a random sample of 1,000
  births, let x be the number that occur by
  Caesarian section.
• A) mean np1,000(.22)220
• B) Std dev13.10
• D) Find

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5.60 continued
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Homework for Section 5.5

• Pages 248-249, 5.54, 5.56, 5.61, 5.67, 5.69

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The Exponential Distribution ORWaiting Time
Distribution

• Situations that Produce an Exponential
  Distribution
• 1) Length of time between emergency arrivals at a
  hospital
• 2) Length of time between break-downs of
  machinery
• 3) Length of time between catastrophic events
• 4) Length of time between sightings of an
  endangered species

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Probability Distribution, Mean, and Standard
deviation for an Exponential Random Variable x
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Finding the Area, A, to the right of a number, a,
for an Exponential Distribution
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Example- Page 253, 5.73

• With
• Determine

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5.73 continued

• B)

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Homework Section 5.6

• Pages 253-254
• 5.74, 5.75, 5.80, 5.85