Question

Let the mean success rate of a Poisson process be 12 successes
per hour.

**a.** Find the expected number of successes in a 19
minutes period. **(Round your answer to 4 decimal
places.)**

**b.** Find the probability of at least 2 successes in
a given 19 minutes period. **(Round your answer to 4 decimal
places.)**

**c.** Find the expected number of successes in a two
hours 30 minutes period. **(Round your answer to 2 decimal
places.)**

**d.** Find the probability of 23 successes in a given
two hours 30 minutes period. **(Do not round intermediate
calculations. Round your final answer to 4 decimal
places.)**

Answer #1

X ~ Poisson ()

Where = 12 successes per hour.

Poisson probability distribution is

P(X) = e^{-}^{X} /
X!

a)

E(X) = 12* 19 / 60 = **3.8**

b)

P(X >= 2) = 1 - P(X <= 1)

= 1 - [ P(X = 0) + P(X = 1) ]

= 1 - [e^{-3.8} + e^{-3.8} * 3.8 ]

= **0.8926**

c)

In 2 hour 30 minutes, there are 2 * 60 + 30 = 150 minutes.

E(X) = 12 * 150 / 60 = **30**

d)

P(X = 23) = e^{-30} * 30^{23} / 23!

= **0.0341**

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