Kichter SCaie: yol Wly not 10. Earthquakes in the World Various sources provide

Question

Kichter SCaie: yol Wly not 10. 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. Richter scale, would it make sense to report that this is a year with an unusual number of earthquakes? Why or why not? 11. Radioactiye Decay Radioactive atoms are unstable because they have too much energy.

Explanation / Answer

a)

mean number of earthquake=5469/41=133.39

b)er mean =133.39

and std deviaiton =sqrt(133.39)=11.5495

therefore from normal approximation

P(exactly 133 earthquake)=P(X=133)=P(132.5<X<133.5)=P((132.5-133.39)/11.5495<Z<(133.5-133.39)/11.5495)

=P(-0.08<Z<0.01)=0.5040-0.4681 =0.0359

c)

here probabiliy of getting 133 or less earthquake)=P(X<=133)=P(Z<(133.5-133.39)/11.5495)=P(Z<0.01)=0.5040

as probability of that happening is not less than 0.05 level we can not conclude that this is a year with an unusual number of earthquakes.

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