Question

In: Statistics and Probability

The manager of a fast-food restaurant determines that the average time that her customers wait for...

The manager of a fast-food restaurant determines that the average time that her customers wait for service is 5.5 minutes. (a) Find the probability that a customer has to wait more than nine minutes. (Round your answer to three decimal places.)

(b) Find the probability that a customer is served within the first five minutes. (Round your answer to three decimal places.)

(c) The manager wants to advertise that anybody who isn't served within a certain number of minutes gets a free hamburger. But she doesn't want to give away free hamburgers to more than 2% of her customers. What should the advertisement say? (Give your answer to the nearest integer that satisfies the conditions.) "If you aren't served within ???? minutes, you get a free hamburger."

Solutions

Expert Solution

Answer to the question)

Since the waiting time follows poisson distribution

given mean time = 5.5

Lambda = 5.5

.

Part a)

P(x > 9) = 1 - P(x < =9)

P(x < = 9) = P(x=0) + P(x=1) + P(x=2) + ..... + P(x=9)

The formula to be used for manual working is :

P(X=x) = e^-(λ) * (λ)^x / x!

we got λ = 5.5

using technology , we can use the excel function as follows to find P(x < = 9)

=POISSON(9,5.5,1)

We get P(x < =9) = 0.9462

P(x>9) = 1 - 0.9462

P(x>9) =0.0538

.

Part b)
P(x<= 5) = P(x=0) + P(x=1) + P(x=2) + P(x=3) + P(x=4) + P(x=5)

Using excel function =poisson(5,5.5,1)

P(x<=5) = 0.5289

.

Part c)

P(X > x) = 2% ~0.02

P(X < =x) = 1 - P(x > x)

P(X < =x) = 1 - 0.02 = 0.98

we know that for more than 9 minutes the probability is 0.05

Thus x has to be larger than 9

by hit and trial method we can plug in x = 10

we get P( x> 10) = 0.025 ~2.5%

[use excel function =1-POISSON(10,5.5,1)]

Next plug in x = 11

we get P(x > 11) = 0.011 ~1.1%

[use excel function =1-POISSON(11,5.5,1)]

Thus we conclude that the time must be 10 minutes

it must state that if you aren't served within 10 minutes you get a free hamburger


Related Solutions

A fast-food restaurant determines the cost and revenue models for its hamburgers. A fast-food restaurant determines...
A fast-food restaurant determines the cost and revenue models for its hamburgers. A fast-food restaurant determines the cost and revenue models for its hamburgers. C = 0.8x + 7100,     0 ≤ x ≤ 50,000 R = 1 10,000 (66,000x − x2),     0 ≤ x ≤ 50,000 (a) Write the profit function for this situation. P =   (b) Determine the intervals on which the profit function is increasing and decreasing. (Enter your answers using interval notation.) increasing     decreasing     (c) Determine how many hamburgers...
The average time between arrivals of customers at a fast food restaurant drive through is 4...
The average time between arrivals of customers at a fast food restaurant drive through is 4 minutes. Assuming an exponential distribution, what is the probability that the next customer arrives in less than 3 minutes? Group of answer choices 39.35% 52.76% 47.24% 60.65% 75.00% If u can please show excel input
The manager of a local fast-food restaurant is concerned about customers who ask for a water...
The manager of a local fast-food restaurant is concerned about customers who ask for a water cup when placing an order but fill the cup with a soft drink from the beverage fountain instead of filling it with water. The manager selected a random sample of 50 customers who asked for a water cup when placing an order and found that 8 of those customers filled the cup with a soft drink from the beverage fountain. (a) Find the sample...
In a drive-thru fast food restaurant, customers arrive with an interarrival time of 6 minutes. The...
In a drive-thru fast food restaurant, customers arrive with an interarrival time of 6 minutes. The drive-thru operates in just a single file line so only one customer’s order is processed at once. The drive-thru has an average service time of 4 minutes. What is the steady-state utilization of the drive-thru? What is the average time in system per customer? What is the probability of there being exactly 1 customer in the queue?
The manager of a fast-food restaurant wants to reduce the proportion of drive-through customers who have...
The manager of a fast-food restaurant wants to reduce the proportion of drive-through customers who have to wait longer than 2 minutes to receive their food after placing an order. Based on store records, the proportion of customers who had to wait longer than 2 minutes was p = 0.63. To reduce this proportion, the manager assigns an additional employee to assist with drive-through orders. During the next month, the manager will collect and random sample of drive through times...
In a benchmark study, a fast food restaurant had an average service time of 2.1 minutes....
In a benchmark study, a fast food restaurant had an average service time of 2.1 minutes. Assume that the service time for the fast food restaurant has an exponential distribution. (Round your answers to four decimal places.) (a) What is the probability that a service time is less than or equal to one minute? (b) What is the probability that a service time is between 30 seconds and one minute? (c) Suppose the manager of the restaurant is considering instituting...
In a benchmark study, a fast food restaurant had an average service time of 2.1 minutes....
In a benchmark study, a fast food restaurant had an average service time of 2.1 minutes. Assume that the service time for the fast food restaurant has an exponential distribution. (Round your answers to four decimal places.) What is the probability that a service time is less than or equal to one minute? What is the probability that a service time is between 45 seconds and one minute? Suppose the manager of the restaurant is considering instituting a policy such...
The average wait time to get seated at a popular restaurant in the city on a...
The average wait time to get seated at a popular restaurant in the city on a Friday night is 7 minutes. Is the mean wait time less for men who wear a tie? Wait times for 12 randomly selected men who were wearing a tie are shown below. Assume that the distribution of the population is normal. 6, 8, 6, 8, 8, 5, 7, 4, 7, 6, 4, 7 What can be concluded at the the α = 0.01 level...
The average wait time to get seated at a popular restaurant in the city on a...
The average wait time to get seated at a popular restaurant in the city on a Friday night is 11 minutes. Is the mean wait time greater for men who wear a tie? Wait times for 15 randomly selected men who were wearing a tie are shown below. Assume that the distribution of the population is normal. 10, 10, 12, 9, 12, 10, 13, 13, 13, 9, 13, 13, 13, 12, 9 What can be concluded at the the α...
Think about your favorite restaurant or fast-food restaurant. The general manager of that restaurant has hired...
Think about your favorite restaurant or fast-food restaurant. The general manager of that restaurant has hired you to help classify all the costs that are involved in running the restaurant and keeping the customers satisfied. Think about its business operations as you answer the following questions. Describe all business activities from the time a customer arrives to the time that customer departs. List all costs you can identify with the separate activities described in question 1. Classify each cost from...
ADVERTISEMENT
ADVERTISEMENT
ADVERTISEMENT