In this problem we would you use the Poisson distribution:
The formula is: p(k) = Pr ( = k) = e^- λ λ^k/k!
Where k is
equal to 0, 1, 2…
λ = to the mean, therefore it is 4.0
a.
k = 0
p(0) = e^-4 4^0/0! = 0.0183
b.
< 2
< 2, use the
additivity probability
= e^-4 4^0/0! + e^-4 4^1/1! + e^-4 4^2/2!
= 0.0916
c.
> 7
Use the probability of complementary events
=1 - (P( =0) + P(
=1) + P( =2) + P( = 3) + +P(
=4) + P( =5) + P( =6) + P(
=7)) = 0.0511
