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

Question

Let the mean success rate of a Poisson process be 12 successes per hour. a. Find the expected number of successes in a 29 minutes period. (Round your final answer to 1 decimal place.) Expected number of successes? b. Find the probability of at least 2 successes in a given 29 minutes period. (Round your answer to 4 decimal places.) Probability? c. Find the expected number of successes in a one hour 48 minutes period. (Round your final answer to 1 decimal place.) Expected number of successes d. Find the probability of 16 successes in a given one hour 48 minutes period. (Round your answer to 4 decimal places.) Probability?

Explanation / Answer

1)

expected number of successes in a 29 minutes period =12*29/60=5.8

b) probability of at least 2 successes in a given 29 minutes

=P(X>=2) =1-P(X<=1)=1-(P(X=0)+P(X=1)) =1-(e-5.8*5.80/0!+e-5.8*5.81/1!)=0.9794

c)

expected number of successes in a one hour 48 minutes period =12*108/60=21.6

d)probability of 16 successes in a given one hour 48 minutes period =e-21.6*21.616/16! =0.0447

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