Question

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?

Answer 1

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