An impulse load occurs on the average of 122 times per hour

An impulse load occurs on the average of 12.2 times per hour. What are the probabilities of observing in a 30-minute span of time: (a) zero impulses, (b) one impulse, (c) eight impulses, (d) twelve impulses, and (e) fifteen impulses?

Solution

In 1 hour an impulse load occurs on an average of 12.2
When the time period is halved the occurance of impulse load doubles
=> in 30 minutes there would be = 12.2*2 = 24.4 impulse loads

a> P(0 impulses) = favourable cases/total cases
in 3 minutes we get 24.4 impulses so we would not get 0 as a favourable case

=> P(0 impulse) = 0/24.4= 0

b> P(1 impulse) = favourable cases/total cases = 1/24.4

c> P(8 impulse) = favourable cases/total cases = 8/24.4 = 2/6.1

d> P(12 impulse) = favourable cases/total cases = 12/24.4 = 3/6.1

e> P(15 impulse) = favourable cases/total cases = 15/24.4