(5). A fire station experiences an average call-out rate of 2.6 every period of
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Question
(5). A fire station experiences an average call-out rate of 2.6 every period of two hours. Using the Poisson distribution, find the probability that in any period of an hour there will be (a) 4callouts (b) more than 4 callouts. P:2,6 The number of radioactive particles emitted in a minute from a meteorite is recorded on a Geiger counter. The mean number is found to be 3.5 per minute. Using the Poisson distribution, find the probability that in any one minute there are (a) no particles, (b) at least 5 particles. (6)Explanation / Answer
#5.
For the period of 1 hour, lambda = 2.6/2 = 1.3
Poisson's Distribution formula,
P(X = x) = (e^-) (^x) / x!
a)
P(X = 4) = (e^-1.3) (1.3^4) / 4! = 0.0324
b)
P(X > 4) = 1 - P(X <= 4)
P(X <= 4) = 0.9893 (Excel formula used to find cumulative probability =POISSON.DIST(4,1.3,TRUE))
P(X > 4) = 1 - 0.9893 = 0.0107
#6.
= 3.5
a)
P(X = 0) = (e^-3.5) (3.5^0) / 0! = 0.0302
b)
P(X >= 5) = 1 - P(X <= 4)
P(X <= 4) = 0.7254
P(X >= 5) = 1 - 0.7254 = 0.2746
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