Example 4.31 from Statistics, 4.6 Poisson Distribution (Optional)

Poisson Distribution (Optional): example 4.31

On May 13, 2013, starting at 4:30 p.m., the probability of low seismic activity for the next 48 hours in Alaska was reported as about 1.02 percent. Use this information for the next 200 days to find the probability that there will be low seismic activity in 10 of the next 200 days. Use both the binomial and Poisson distributions to calculate the probabilities. Are they close?

Work it out on paper first. Then open the solution one step at a time, and stop as soon as you can finish on your own.

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Solution
Let X = the number of days with low seismic activity. We are asked to find the probability over the next 200 days. Probability is given for a 48-hour period.
- n = 200 days = 100 48-hour periods
Using the binomial distribution
- P(x = 10) = binompdf(100, .0102, 10) ≈ .0000000076
Using the Poisson distribution
- Calculate μ = np = 100(.0102) ≈ 1.02
- P(x = 10) = poissonpdf(1.02, 10) ≈ .000000121
We expect the approximation to be good because n is large (greater than 20) and p is small (less than .05). The results are close—both probabilities reported are almost 0.

How did it go?

Solution

Solution