Emails arrive at an average rate of 9 per hour.
A. What is the probability that more than 5 emails arrive over the next hour?
B. What is the probability that the next email arrives within 5 minutes?
a)
X ~ Poi ( )
Where = 9 per hour.
Poisson probability distribution is
P(X) = e-X / X!
So,
P(X > 5) = 1 - P(X <= 5)
= 1 - POISSON.DIST( x , mean, cumulative)
= 1 - POISSON.DIST ( 5 , 9 , TRUE)
= 1 - 0.1157
= 0.8843
b)
This is weighting time distribution.
Where
X ~ EXP ( )
for 1 minute = 9 / 60
So,
For 5 min,
= (9 * 5) / 60 = 0.75
Using exponential distribution,
P(X < x) = 1 - e-
P(X < 5) = 1 - e-0.75
= 0.5276
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