Question

In: Statistics and Probability

During an eight-hour shift, the proportion of time Y that a sheet-metal stamping machine is down...

During an eight-hour shift, the proportion of time Y that a sheet-metal stamping machine is down for maintenance or repairs has a beta distribution with α = 1 and β = 2. That is,

f(y) =

2(1 − y),   0 ≤ y ≤ 1,
0, elsewhere.

The cost (in hundreds of dollars) of this downtime, due to lost production and cost of maintenance and repair, is given by

C = 10 + 30Y + 3Y2.

Find the mean and variance of C. (Round your answers to two decimal places.)

Solutions

Expert Solution


Related Solutions

IN AN 8 HOUR SHIFT Stage A 20 cars per hour               Initial set up time of...
IN AN 8 HOUR SHIFT Stage A 20 cars per hour               Initial set up time of 20 minute when changing the car model or size Stage B 20 cars per hour               Must be shut down for maintenance and cleaning for 30 minute after every 90 minute of operation Stage C 18 cars per hour               More customization, but no setups Where would you place the buffers and what should the buffer capacity in terms of the number of cars? Assume a...
1. Use a graph to explain why overtime wages are higher than the regular eight-hour shift...
1. Use a graph to explain why overtime wages are higher than the regular eight-hour shift wages. Explain why managers offer higher overtime wages. 2. Use a graph to explain economies of scale and why this is important to a manager
1. If a company can identify times of the day during an 8 hour work shift...
1. If a company can identify times of the day during an 8 hour work shift when accidents are most likely to occur extra precautions can be instituted during those times. A random sampling of the accident report records over the last year at the factory gives the following frequency of occurrence of accidents during the different hours of the work shift. Can it be concluded based upon the data in the table that the proportions of accidents are equal...
A can company reports that the number of breakdowns per 8-hour shift on its machine operated...
A can company reports that the number of breakdowns per 8-hour shift on its machine operated assembly line follows a Poisson distribution with a mean of 1.5. What is the probability of exactly three breakdowns on the midnight shift? What is the probability of greater than two breakdowns in one hour? What is the probability that the time between two successive breakdowns is at most three hours? If two hours have gone by without a breakdown, what is the probability...
Taxi drivers work in 12-hour shifts, with most of them having shift-change time around 5pm. In...
Taxi drivers work in 12-hour shifts, with most of them having shift-change time around 5pm. In other words, there are two shifts: 5am-5pm (day shift) and 5pm-5am (night shift). Do dayshift taxi drivers earn more than night-shift taxi drivers? What economic theories and factors would you use to answer this question? Discuss.
1. During your 12-hour shift from 7p – 7a, what is your patient’s INTAKE and OUTPUT...
1. During your 12-hour shift from 7p – 7a, what is your patient’s INTAKE and OUTPUT (see below)?* 2000-0600: Jevity 50 mL/hr, 0615: 50 cc free water flush, 2100-0215: Two 250 mL of red blood cells, 0115: 20 cc saline flush IV, 0300: Zosyn IV 50 mL, 0400: 10 cc saline flush IV, Continuous fluids: Heparin 10 mL/hr & Normal Saline 100 mL/hr ------ Ileostomy: 300 mL, NG suction: 50 cc, Urine: 1850 mL, Wound vac: 100 cc
The amount of time customers wait in line during hour at the bank follows a normal...
The amount of time customers wait in line during hour at the bank follows a normal distribution with a mean of 8.5 minutes and standard deviation of 2.2 minutes. During Peak hours at the bank, what is the probablity a randomly selected person will wait: a. at least 12 minutes? b.no more than 6 minutes? c.between 7 and 10 minutes? d. How many minutes should the bank advertise for service so that no more than 4% of its customers will...
The metropolitan bus company claims that the mean wait time for a bus during rush hour...
The metropolitan bus company claims that the mean wait time for a bus during rush hour is less than 7 minutes. A random sample of 20 waiting times has a mean of 5.6 minutes with a standard deviation of 2.1 minutes. At a= 0.01, test the bus company’s claim. Assume the distribution is normally distributed.
The Metropolitan Bus Company claims that the mean waiting time for a bus during rush hour...
The Metropolitan Bus Company claims that the mean waiting time for a bus during rush hour is less than 10 minutes. A random sample of 20 waiting times has a mean of 8.6 minutes with a sample standard deviation of 2.1 minutes. At ? = 0.01, test the bus company's claim. Assume the distribution is normally distributed. - critical value z0 = -2.326; standardized test statistic ? -2.981; reject H0; There is sufficient evidence to support the Metropolitan Bus Company's...
The number of buses that arrive at a bus stop during a one-hour time span can...
The number of buses that arrive at a bus stop during a one-hour time span can be modeled as a Poisson process with rate λ (see Remark below). Now suppose a passenger has just arrived at the bus stop and starts waiting. Let Y be the time (in unit of hours) she needs to wait to see the first bus. (a) Is Y a discrete or continuous random variable? Find the set of all possible values of Y . (b)...
ADVERTISEMENT
ADVERTISEMENT
ADVERTISEMENT