Question

Let the mean success rate of a Poisson process be 11 successes per hour.

c. Find the expected number of successes in a three hours period. (Round your answer to 2 decimal places.) X Answer is complete but not entirely correct. Expected number of successes 44.00 d. Find the probability of 28 successes in a given three hours period. (Do not round intermediate calculations. Round your final answer to 4 decimal places.) Probability

Answer 1

X ~ Poi($\lambda$)

Where $\lambda$ = 11 per hour

a)

For 3 hour period , $\lambda$ t = 11 * 3 = 33

E(X) = $\lambda$ t = 33

b)

P(X) = e^-$\lambda$t * ($\lambda$t)^X / X!

P(X = 28) = e^-33 * 33²⁸ / 28!

= 0.0504