Use the Poisson distribution to find the indicated probabilities.

Earthquakes in the United States Various sources provide different earthquake data, but assume that for a recent 4l-year period in the United States, there were 268 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 is at least one earthquake in the United States that measures 6.0 or higher on the Richter scale.

c. Is it unlikely to have a year without any earthquakes that measure 6.0 or higher on the Richter scale? Why or why not?

Answer:

Step 1 of 2</p>

It is given that number of earthquakes occurred in united states in 41 years is 268 and n = 41 years.

a. The mean number of earthquakes per year.

By dividing the number of earthquakes with number of years will get mean number of earthquakes per year.

Mean number of earthquakes = = 6.5365