Car security alarms go off at a mean rate of 4.0 per hour in a large costco parking lot. find the probability that in an hour there will be (round your answers to 4 decimal places.) probability (a) no alarms .0183 correct (b) fewer than two alarms .0916 correct (c) more than seven alarms .0511 correct

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