Question

Find each Poisson probability, using a mean arrival rate of 10 arrivals per hour.

  

(a)	Seven arrivals. (Round your answer to 4 decimal places.)

  

Poisson probability

  

(b)	Three arrivals. (Round your answer to 4 decimal places.)

  

Poisson probability

  

(c)	Fewer than five arrivals. (Round your answer to 4 decimal places.)

  

Poisson probability

  

(d)	At least 11 arrivals. (Round your answer to 4 decimal places.)

  

Poisson probability

Answer 1

We are given to find the Poisson probability.

we know that the probability mass function:

where

is the random variable

the average rate of success. (Here 10)

(a) Probability of seven arrivals i.e.

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(b) Similarly, for three arrivals ()

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(c) For fewer than or less than 5 arrivals i.e.

Since Poisson is a discrete distribution:

Similarly,

we get

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(d) Now, for at least 11 arrivals: i.e.

as for at least 11, we can subtract probability for fewer than11arrivals from the total sum of probability (i.e. 1).

Therefore,

Similarly, on solving as above we get:

Now,

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