Question

Suppose there is a place in Japan where earthquakes, though occurring randomly, occurs an average of 4 times per month.

(a) What is the probability the earthquake occurs fewer than three times in a month?

(b) What is the probability the earthquake occurs 10 times in two months?

(c) What is the probability that someone will experience the earthquake within the first week of arriving at that place? (For the sake of this problem, assume that a week is exactly 1/4 of a month).

(d) Suppose there is a company that offers one-week packages to experience the earthquake, but of course, they cannot guarantee that the earthquake will occur during the week. If 100 different people book these packages at different times, what is the probability that more than half of them will experience the earthquake?

Answer 1

Mean/Expected number of events of interest: λ =                4

X	P(X)
0	0.0183
1	0.0733
2	0.1465

p(x<3) = p(0)+p(1)+p(2)

=0.2381

..............

b)

Mean/Expected number of events of interest: λ =                8
p(x=10) = 0.0993

........

c)

Mean/Expected number of events of interest: λ =                1
p(x=1) = 0.3679

................

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