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WARM UP

WARM UP. The Consumer Affairs Corporation finds that 44% of all complaints about fraudulent purchases are valid. If the Corporation received 3,786 complaints find the mean , variance , and standard deviation. POISSON DISTRIBUTION. SECTION 6.7. POISSON DISTRIBUTION.

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WARM UP

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  1. WARM UP • The Consumer Affairs Corporation finds that 44% of all complaints about fraudulent purchases are valid. If the Corporation received 3,786 complaints find the mean, variance, and standard deviation.

  2. POISSON DISTRIBUTION SECTION 6.7

  3. POISSON DISTRIBUTION Each success is independent Probability of success is very small

  4. Poisson Distribution formula e = 2.718… = mean x = number of successes or trials

  5. SNOW DAYS (soon please!) • Salesianum averages about three snow days each school year. What is the probability that there will be exactlyfive snow days this school year? e = 2.718… mean = 3 x = exactly 5 = 0.1008 or about 10%

  6. UFOs • The average number of UFO sightings from Delaware is about 7 a year. Assuming a Poisson Distribution, what is the probability that • There are exactly six sightings? • There are at most two sightings? • There are at least five sightings? = 0.1490 about 15%

  7. UFOs • The average number of UFO sightings from Delaware is about 7 a year. Assuming a Poisson Distribution, what is the probability that • There are at most two sightings? x = 0, 1, 2 = 0.000911 = 0.000911 = 0.0296 or about 3% = 0.00638 = 0.00638 = 0.02234 = 0.02234

  8. UFOs • The average number of UFO sightings from Delaware is about 7 a year. Assuming a Poisson Distribution, what is the probability that • There are at least five sightings? x = 5, 6, 7 = 0.1277 = 0.1277 = 0.4257 or about 43% = 0.1490 = 0.1490 = 0.1490 = 0.1490

  9. Mean, variance, and standard deviation • For a Poisson Distribution, the mean = variance. • And I will give you the mean! • Standard deviation =

  10. Homicides • Delaware averages about 30 homicides each year, mostly in NCC. Assuming a Poisson process, find the variance and standard deviation. Mean = variance Mean = 30 = variance

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