Question

Poisson distribution Exercise

Q3. During the 30-year period 1959-1988, a total of 138 tornadoes were reported in New York State. Let X denote the number of tornadoes reported per year in New York State and assume that X follows a Poisson distribution. Estimate the probability that, during a given year, New York State reports:

a. No tornadoes

b. At most three tornadoes

c. More than two but not more than five tornadoes

d. At least six tornadoes

Express probabilities to six decimal places

***PLEASE SHOW ALL WORK****

Thank you!!

Answer 1

Ans:

Average number of tornadoes per year=138/30=4.6

Use Poisson distribution:

P(x=k)=exp(-4.6)*(4.6^k/k!)

a)

P(x=0)=exp(-4.6)*(4.6^0/0!)=0.010052

b)

P(at most 3)=P(x<=3)

=exp(-4.6)*(4.6^0/0!+4.6^1/1!+4.6^2/2!+4.6^3/3!)

=0.325706

c)

P(2<x<=5)=P(x=3)+P(x=4)+P(x=5)

=exp(-4.6)*(4.6^3/3!+4.6^4/4!+4.6^5/5!)

=0.163068+0.187528+0.172526

=0.523121

d)

P(at least 6)=P(x>=6)=1-P(x<=5)

=1-exp(-4.6)*(4.6^0/0!+4.6^1/1!+4.6^2/2!+4.6^3/3!+4.6^4/4!+4.6^5/5!)

=0.314240