16. In the Ames Bank (open 24h every day) 5 customers arrive on average during a

Question

16. In the Ames Bank (open 24h every day) 5 customers arrive on average during an hour. For the following questions state each time which random variable you use and what distribution assumption you make. (a) What is the probability that during an hour no customer arrives? (b) What is the probability that during an hour more than 7 customers arrive? (c) What is the probability that there's more than 30 minutes between the 2nd and 3'd customer on New Year's Day? (d) Starting at some time 0. What is the probability that the first customer arrives after exactly 10 min? Within the first ten minutes? (e) How many minutes do you expect to wait on average between arrivals? (f) How many customers do you expect to arrive within 3 hours?

Explanation / Answer

Question 16

Customers arrival rate = 5

so the given distribution is poisson

(a) Here if X is the numbers of arrivals in one hour on a random day

Pr(X = 0) = POISSON( 0 ; 5) = e-5 50/0! = 0.0067

(b) Pr(X > 7) = 1 - POISSON (X < = 7 ; 5) = 0.86666

(c) Here it is asking that 3rd customer have taken more than 30 minutes to come.

So, expected arrival in 30 minutes = 5/2 = 2.5

so, there is no arrival in 30 minutes so

Pr(X = 0 ; 2.5) = e-2.5 2.50/0! 0.0821

(d) Numbeer of expected customers in 10 mins = 10/60 * 5 = 5/6

so, Pr(there will be no customers in 10 mins) = POISSON (X = 0 ; 5/6) = e-5/6 (5/6)0/0! = 0.4346

Pr(there will be a customer in less than 10 mins) = 1 - 0.4346 = 0.5654

(e) Here interarrival times = 60 minutes/5 = 12 minutes

(f) Here expected number of customers to arrive in 3 hours = 3 * 5 = 15

Related Questions

Navigate

• Browse (All)
• Browse 1
• Subjects

---

---

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