Question

In: Statistics and Probability

A restaurant is about to close, but it must wait until all 8 remaining customers have...

  1. A restaurant is about to close, but it must wait until all 8 remaining customers have left. Starting now, each customer’s remaining time in the restaurant is exponentially distributed with mean fifteen minutes. If the customers leave independently of one another, find the probability that (a) after 2 hours the restaurant is still open; (b) after 1 hour, the restaurant is still waiting on exactly 2 customers.

Solutions

Expert Solution

a) Probability that after 2 hours that is 120 minutes, the restaurant is still open is computed here as:

= 1 - Probability that all 8 remaining customers leave within 2 hour period

Therefore 0.002681 is the required probability here.

b) Probability that after an hour that is 60 minutes, there are exactly 2 customers left is computed here as:

= Number of ways to choose 6 of the 8 customers * Probability that 6 out of the 8 customers finish in the first 60 minutes * Probability that 2 customers finish after 60 minutes

Therefore 0.008407 is the required probability here.

orchestra answered 2 years ago
Next > < Previous

Related Solutions

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...
An automotive part must be machined to close tolerances to be acceptable to customers. Production specifications...
An automotive part must be machined to close tolerances to be acceptable to customers. Production specifications call for a maximum variance in the lengths of the parts of 0.0006. Suppose the sample variance for 40 parts turns out to be s2 = 0.0007. Use α = 0.1 to test whether the population variance specification is being violated. Select one: a. Test statistic = 51.39, reject H0 b. Test statistic = 51.39, can't reject H0 c. Test statistic = 45.5, reject...
As the owner of a restaurant, you must make decisions about the location of your restaurant...
As the owner of a restaurant, you must make decisions about the location of your restaurant and the equipment and furniture needed to operate your restaurant. Would you prefer to buy or lease your building? Also, discuss whether you would prefer to buy or lease your equipment and furniture. What benefit do you see in your choices?
As the owner of a restaurant, you must make decisions about the location of your restaurant...
As the owner of a restaurant, you must make decisions about the location of your restaurant and the equipment and furniture needed to operate your restaurant. Would you prefer to buy or lease your building? Also, explain whether you would prefer to buy or lease your equipment and furniture. What benefit do you see in your choices? 200 words or more
As the owner of a restaurant, you must make decisions about the location of your restaurant...
As the owner of a restaurant, you must make decisions about the location of your restaurant and the equipment and furniture needed to operate your restaurant. Would you prefer to buy or lease your building? Also, discuss whether you would prefer to buy or lease your equipment and furniture. What benefit do you see in your choices?
Research by First Bank of Illinois revealed that 8 percent of its customers wait more than...
Research by First Bank of Illinois revealed that 8 percent of its customers wait more than five minutes to do their banking when not using the drive-through facility. Management considers this reasonable and will not add more tellers unless the proportion becomes larger than 8 percent. The branch manager at the Litchfield Branch believes that the wait is longer than the standard at her branch and requested additional part-time tellers. To support her request she found that, in a sample...
A service station advertises that customers will have to wait no more than 30 miniutes for...
A service station advertises that customers will have to wait no more than 30 miniutes for an oil change. A sample of 25 oil changes has a standard deviation of 5.2 minutes. a) Find the 95% confidence interval of the population variance of the time spent waiting for oil change. b) Find the 95% confidence interval of the population standard deviation of the time spent waiting for oil change.
Hey service station advertises that customers will have to wait no more than 30 minutes for...
Hey service station advertises that customers will have to wait no more than 30 minutes for an oriole change a sample of 28 oil change has a standard deviation of five. Two minutes find the 95% confidence interval of the population variance and standard deviation of the time spent waiting for an oil change
A restaurant manager asks all of the customers this month to take an online survey (and...
A restaurant manager asks all of the customers this month to take an online survey (and get a free appetizer their next visit). It turns out that 241 customers actually take the survey, and of these 209 were ''extremely satisfied'' with their visit. Set up an approximate 95% confidence interval for the proportion of all the restaurant's customers that say they were ''extremely satisfied'' with their visit.. Select only one of the boxes below. A. The Normal curve cannot be...
I would guess that each of you have been to a fast-food restaurant. Think about all...
I would guess that each of you have been to a fast-food restaurant. Think about all of the aspects of the operation procedures used to take, process, and fill an order and deliver the order to the customer. Based on what you have observed during your visit to one of these restaurants, identify at least three variable and three fixed costs. Can you identify any potential mixed costs? Why is the restaurant willing to sell a large drink for only...
ADVERTISEMENT
Subjects
ADVERTISEMENT
Latest Questions
ADVERTISEMENT