Alice has two identical personal computers, which she never uses at the same time. She uses one PC at a time and the other is a backup. If the one she is currently using fails, she turns it off, calls the PC repairman and turns on the backup PC. The time until either PC fails when it is in use is exponentially distributed with a mean of 50 hours. The time between the moment a PC fails until the repairman comes and finishes repairing it is also exponentially distributed with a mean of 3 hours. What is the probability that Alice is idle because neither PC is operational?

Alice has two identical personal computers, which she never uses at the same time. She uses one PC at a time and the other is a backup. If the one she is currently using fails, she turns it off, calls the PC repairman and turns on the backup PC. The time until either PC fails when it is in use is exponentially distributed with a mean of 50 hours. The time between the moment a PC fails until the repairman comes and finishes repairing it is also exponentially distributed with a mean of 3 hours. What is the probability that Alice is idle because neither PC is operational?

College Algebra

1st Edition

ISBN:9781938168383

Author:Jay Abramson

Publisher:Jay Abramson

Chapter6: Exponential And Logarithmic Functions

Section6.1: Exponential Functions

Problem 62SE: A scientist begins with 100 milligrams of aradioactive substance that decays exponentially. After 35...

See similar textbooks

Similar questions

Find an exponential equation that passes throughthe points (0,4) and (2,9).
Explain why the values of an increasing exponentialfunction will eventually overtake the valuesof anincreasing linear function.
Does a linear, exponential, or logarithmic model best fit the data in Table 2? Find the model.
A scientist begins with 100 milligrams of aradioactive substance that decays exponentially. After 35 hours, 50 mg of the substance remains. How manymilligrams will remain after 54 hours?
What might a scatterplot of data points look like if it were best described by a logarithmic model?
Each machine on Widgetco’s assembly line gets out ofwhack an average of once a minute. Laborers are assignedto reset a machine that gets out of whack. The companypays each laborer cs dollars per hour and estimates that eachhour of idle machine time costs the company cm dollars inlost production. Data indicate that the time betweensuccessive breakdowns of a machine and the time to reset amachine are exponential. Widgetco plans to assign eachworker a certain number of machines to watch over andrepair. Let M total number of Widgetco machines, w number of laborers hired by Widgetco, and R Mw machines assigned to each laborer.a Express Widgetco’s hourly cost in terms of R and M.b Show that the optimal value of R does not dependon the value of M.c Use calculus to show that costs are minimized bychoosingR d Suppose cm 78¢ and cs $2.75. Widgetco has 200 machines, and a laborer can reset a machine in an aver-age of 7.8 seconds. How can Widgetco minimize costs? e In parts (a)–(d), we have…
The Regency Hotel has enough space at its entrance for six taxicabs to line up, wait for guests,and then load passengers. Cabs arrive at the hotel every 8 minutes; if a taxi drives by the hoteland the line is full, it must drive on. Hotel guests require a taxi every 5 minutes, on average. Ittakes a cab driver an average of 3.5 minutes to load passengers and luggage and leave the hotel(exponentially distributed). What is the probability that the line will be full when a cab drives by, causing it to drive on?
The small mail-order firm Sea’s Beginning has one phone line. An average of 60 people per hour call in orders, and it takes an average of one minute to handle a call. Time between calls and time to handle calls are exponentially distributed. If the phone line is busy, Sea’s Beginning can put up to c - 1 people on hold. If c - 1 people are on hold, a caller gets a busy signal and calls a competitor. Sea’s Beginning wants only 1% of all callers to get a busy signal. How many people should it be able to put on hold, that is, what is the required value of c?
The Bay City Police Department has eight patrol cars that are on constant call 24 hours per day. A patrol car requires repairs every 20 days, on average, according to an exponential distribution. When a patrol car is in need of repair, it is driven into the motor pool, which has a repair person on duty at all times. The average time required to repair a patrol car is 18 hours (exponentially distributed). Determine the average time a patrol car is not available for use and the average number of patrol cars out of service at any one time. Indicate whether the repair service seems adequate.
A poultry raiser harvests an average of 300 eggs per day. He has recently experimented with the different types of poultry feeds. As a result, he noticed some fluctuation in the number of eggs laid by the chickens, which is neither clearly higher nor lower than previous weeks. He decides to find out whether there might be a significant change in the number of eggs laid by the chickens. He records his harvest of eggs for 20 days. He finds that the average per day is 290 eggs with a standard deviation of 15. At 5% level of significance, what did the poultry raiser find out?
A news article states that the number of people infected with a particular virus has grown by 20% in one week which means 56 people became infected that week. 1. If the growth is linear, how many more people will be infected in one more week? If the growth is exponential, how many more people will be infected in one more week?
A poultry raiser harvests an average of 300 eggs per day. He has recently experimented with different types of poultry feeds. As a result, he noticed some fluctuations in the number of eggs laid by the chickens, which is neither clearly higher nor lower than previous weeks. He decides to find out if there might be a significant change in the number of eggs laid by the chickens. He records his harvest of eggs for 20 days. He finds that the average per day is 290 eggs with a standard deviation of 15. At 5% Level of Significance, what did the poultry raiser concludes?