A hair salon provides low-cost haircuts at a shopping center in Boise, Idaho. During the day, customers arrive at an average rate of 8 per hour following a Poisson distribution. After a customer is in a cosmetician's chair, it takes an average of 21 minutes for the haircut to be completed, with the actual service time following an exponential distribution. (Round your answers to four decimal places.) (a) If there are 3 cosmetician's on duty, how many customers are typically waiting for service?  ______ customers How long will customers have to wait on average (in minutes) before receiving service?  ______ minutes (b) If there are 4 cosmetician's on duty, how many customers are typically waiting for service?  ______ customers How long will customers have to wait on average (in minutes) before receiving service?  ______ minutes (c) If there are 5 cosmetician's on duty, how many customers are typically waiting for service?  ______ customers How long will customers have to wait on average (in minutes) before receiving service?  ______ minutes (d) If you managed this store, how many cosmetician's would you employ and why?

TKK Products manufactures electric light bulbs. Lab tests show that the distribution of lives (in hours) of these bulbs are N(700,75). Find the proportion of bulbs that will burn as described below Between 750 and 900 hours Between 600 and 800 hours

Many of a bank’s customers use its automatic teller machine to transact business after normal banking hours. During the early evening hours in the summer months, customers arrive at a certain location at the rate of one every other minute. This can be modeled using a Poisson distribution. Each customer spends an average of 85 seconds completing his or her transactions. Transaction time is exponentially distributed. a. Determine the average time customers spend at the machine, including waiting in line and completing transactions. (Do not round intermediate calculations. Round your answer to the nearest whole number.) Average time  _______ minutes b. Determine the probability that a customer will not have to wait upon arriving at the automatic teller machine. (Round your answer to 2 decimal places.) Probability _______ c. Determine the average number of customers waiting to use the machine. (Round your answer to 2 decimal places.) Average number  ______customers

Solve this question using Rstudio. Some previous studies have shown a relationship between emergency-room admissions per day and level of pollution on a given day. A small local hospital finds that the number of admissions to the emergency ward on a single day ordinarily (unless there is unusually high pollution) follows a Poisson distribution with mean = 2.0 admissions per day. Suppose each admitted person to the emergency ward stays there for exactly 1 day and is then discharged. The hospital is planning a new emergency-room facility. It wants enough beds in the emergency ward so that for at least 95% of normal-pollution days it will not need to turn anyone away. What is the smallest number of beds it should have to satisfy this criterion?

A study-aid desk staffed by a graduate student has been established to answer students' questions and help in working problems in your OSCM course. The desk is staffed eight hours per day. The dean wants to know how the facility is working. Statistics show that students arrive at a rate of six per hour and the distribution is approximately Poisson. Assistance time averages 6 minutes, distributed exponentially. Assume population and line length can be infinite and queue discipline is FCFS. a. Calculate the percentage utilization of the graduate student. (Round your answer to 1 decimal place.) b. Calculate the average number of students in the system, including the graduate student service desk. (Round your answer to 1 decimal place.) c. Calculate the average time in the system. (Round your answer to 1 decimal place.) d. Calculate the probability of four or more students being in line or being served. (Round your intermediate calculations to 3 decimal places and final answer to 1 decimal…

A crew is building a series of identical day spas around the United States for a lifestyle company. They build the first one in 160 days from groundbreaking to ribbon-cutting. If the crew's learning curve rate is 97%, it will take nearest 1/10th, to construct the fifth day spa. days, to the

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The table shows the number of students on the track team who run the hurdles and in relays. No student runs in both. Hurdles Relays 7th graders 8 12 8th graders 15 15 Total 23 27 Total 20 30 50 What is the joint relative frequency to the nearest hundredth of boys who run relays?

Mariah Jacobsen is the marketing manager at ABC Electronics, a major consumer electronics supplier in the northwest. Over the last five years, sales of the company's flagship product - the Wizer Anonymizer (the WA) - have been 45000, 45500, 44500, 46000 and 44000 units. This rate of sales is considered average for the product over the last twenty years or so. Ms. Jacobsen believes that the distribution of the WA's sales is normal with a standard deviation of 1500 units. If she were asked to make a forecast of next year's sales to upper management, what is the likelihood that she would be correct if she predicts sales between 43000 and 46000?

Previously, De Anza's statistics students estimated that the amount of change daytime statistics students carry is exponentially distributed with a mean of $0.88. Suppose that we randomly pick 25 daytime statistics students. Find the probability that an individual had between $0.80 and $1.00. Graph the situation, and shade in the area to be determined.