Question

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

Short answer

The probability for $P_B(X=5)=0.01146,P_P(X=5)=0.011925$

Step-by-step solution

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.

Explanation

The variable $X$counts the set of days with moderate earthquake activity.

And use the binomial distribution with $n=100$trials 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

$\mu =n\cdot p=100\cdot 0.0143=1.43$, the following results are obtained:

$P(X=5)=0.011925$

The findings are close since $n$is large and $p$is small.