Problem 10BSC

Use the Poisson distribution to find the indicated probabilities.

Earthquakes in the World Various sources provide different earthquake data, but assume that for a recent 41-year period in the world, there were 5469 earthquakes measured at 6.0 or higher on the Richter scale (based on U.S. Geological Survey data).

a. Find the mean number of earthquakes per year.

b. Find the probability >that in a given year, there are exactly 133 earthquakes that measures 6.0 or higher on the Richter scale.

c. If, in a particular year, there are exactly 133 earthquakes that measure 6.0 or higher on the Richter scale, would it make sense to report that this is a year with an unusual number of earthquakes? Why or why not?

Answer:

Step 1:

Given that,Various sources provide different earthquake data, but assume that for a recent 41-year period in the world, there were 5469 earthquakes measured at 6.0 or higher on the Richter scale.

a). The mean number of earthquakes in the world measuring to a magnitude of 6 or higher is

earthquakes per year.

b). Consider a random variable “x” follows poisson distribution with sample size “n” and proportion “p”.

i,e.X P()

Probability mass function of poisson distribution is given by

P(x) = , x = 0,1,2,...,n.

Where, e is a eulerian number.

e = 2.71828. ( constant value)

The probability that there are exactly 133 earthquakes in the world which measure 6 or higher using the richter scale is

P(x = 133) =

c). No, although the probability that exactly 133 earthquakes occur within a year is very small (0.0346),the number 133 is very close to the mean of 133.4 that this year would be quite ordinary,and it is not unusual.