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Chapter 4: Q. 4.32 (page 271)

On May 13,2013, starting at 4.30PM, the probability of moderate seismic activity for the next 48hours in the Kuril Islands off the coast of Japan was reported at about 1.02%. Use this information for the next 100days to find the probability that there will be low seismic activity in five of the next 100days. Use both the binomial and Poisson distributions to calculate the probabilities. Are they close?

Short Answer

Expert verified

The probability for PB(X=5)=0.01146,PP(X=5)=0.011925

Step by step solution

01

Introduction

Unpredictability is examined using the mathematical language of probability. It's about the likelihood (probability) of something happening. If you throw a fair coin four times, the results are improbable to be two heads and two tails.

02

Explanation

The variable Xcounts the set of days with moderate earthquake activity.

And use the binomial distribution with n=100trials and a probability of success of p=0.0143, the results were as follows:

P(X=5)=0.01146

Just using Poisson process with a mean of

μ=n⋅p=100⋅0.0143=1.43, the following results are obtained:

P(X=5)=0.011925

The findings are close since nis large and pis small.

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