Hebert\'s food trailer in Austin sells Cajun Tacos (go figure ... only in Austin

Question

Hebert's food trailer in Austin sells Cajun Tacos (go figure ... only in Austin would someone eat a Cajun taco) at a profit of $1.00 per taco. Hebert has good qualitative reasons to believe that customers his trailer according to a Poisson process and that P (N_t = n) = (lambda t)^n e^-lambda t/n!, where N_t is the number of arriving customers in [0, t], and lambda is the arrival rate of customers in units of "customers per hour": through observation, Hebert has learned that lambda = 10. What is Hebert's expected lunch hour profit? (Don't freak out. Just remember the three things Wortman told you to always remember and obtain the formula for E [N_t] with t = 1 and lambda = 10.) What is the probability that Hebert will make more than $5.00 over the lunch hour?

Explanation / Answer

A. Herbert's expected lunch hour arrival customer per hour = t = 10 *1 = 10 customers per hour

He get profit of $1.00 per taco and he sells 10 tacos per hour so

E[P] = $ 10.00 per hour

B. Here we have to calculate the probability that He will earn more than $ 5 per hour that means he will have number of customers per hour more than 5.

so Pr ( N>5 ; = 10 and t = 1 hour) = ?

by poission distribution table

Pr ( N > 5 ; = 10 and t = 1 hour) = 0.9707

so it is 97.1% probability that he will earn more than $5 per hour.

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