A worker at an information booth at the O’Hare Airport in Chicago has found (by

Question

A worker at an information booth at the O’Hare Airport in Chicago has found (by collecting data) that he serves an average of 24 customers per hour and notes that he is pretty sure that the arrivals follow a Poisson distribution. He asks his friend to cover for him for an hour while he goes to get a massage. When he returns, his friend insists that he be paid double for the work he did because he is sure that he helped at least 40 customers. According to the Poisson distribution, if the mean is 24 customers/hour, then what is the probability that 40 or more customers arrived in a given hour? (Note - this is not a 'Waiting Lines' question that uses the Excel template, but rather is a question about Poisson arrivals and would use the Poisson equation seen in the lab, text and in class. You will most likely require a spreadsheet to be efficient in answering this question).

0.07% probability

4.6% probability

12.4% probability

0.17% probability

a.

0.07% probability

b.

4.6% probability

c.

12.4% probability

d.

0.17% probability

Explanation / Answer

P(x=40 I Lambda=24) = ((24^40) * e^(-24))/ 40!=0.000748

P(x=41 I Lambda=24) = ((24^41) * e^(-24))/ 41!=0.000438

calculate the probability for next arrivals and add all of them

below is the result

0.001651

Hence none of the option match the answer, please check if the number of customers were 40 or some other number.

Customers Probability 40 0.000748 41 0.000438 42 0.00025 43 0.00014 44 0.00 total

0.001651

Related Questions

Navigate

• Browse (All)
• Browse A
• Subjects

---

---

Integrity-first tutoring: explanations and feedback only — we do not complete graded work. Learn more.