In a company, a mechanic maintains four very important machines in a production process, which usually break down on average every 10 hours. This time between breakdowns has an exponential distribution. The mechanic spends on average 7 hours repairing a loom and its repair time also has an exponential distribution. Determine the average time a machine spends waiting for maintenance.

In a company, a mechanic maintains four very important machines in a production process, which usually break down on average every 10 hours. This time between breakdowns has an exponential distribution. The mechanic spends on average 7 hours repairing a loom and its repair time also has an exponential distribution. Determine the average time a machine spends waiting for maintenance.

A First Course in Probability (10th Edition)

10th Edition

ISBN:9780134753119

Author:Sheldon Ross

Publisher:Sheldon Ross

Chapter1: Combinatorial Analysis

Section: Chapter Questions

Problem 1.1P: a. How many different 7-place license plates are possible if the first 2 places are for letters and...

See similar textbooks

Similar questions

A company is planning to replace all 10,000 of the light bulbs with new energy saving bulbs. These bulbs have a lifetime that follows an exponential distribution with mean of 4,000 hours. If all the companies lights are on nine hours a day and five days a week, approximately how long will it be before the company has to replace the first bulb? Approximately how long, in weeks, will it be before they need to replace the last of these 10.000 bulb?
If the inter-arrival time and service time in a public telephone booth with a single phone follow exponential distributions with means of 10 and 8 minutes respectively, find the average number of callers in the booth at any time.
The lifespan of an oven made by General Electric (GE) has a mean life of 2.03 years, exponentially distributed. GE agrees to pay a full refund (100%) to a buyer if the oven breaks during the first 3 months following its purchase, a 50% refund if it breaks during months 3-12, and a 25% refund if it breaks between months 12-24. There is no refund for ovens that break after 24 months. If GE sells 330 ovens, how many ovens in total would they expect to provide a full or partial refund for? (Round up to the nearest whole oven) For a standard normal distribution, find: P(z > c) = 0.4395 Find c.
Suppose that the length of long distance phone calls, mea- sured in minutes, is known to have an exponential distribution with the average length of a call equal to 15 minutes. Find the CDF.
There is a 40% chance that a customer will choose Diner A for takeouts and a probability of 60% that he/she will choose Diner B. If he/she orders from Diner A, 12 minutes after placing the order, the remaining time it takes for the food to be delivered is exponentially distributed with an average of 14 minutes. If she orders from Diner B, 17 minutes after placing the order, the time it takes for the food to arrive is exponentially distributed with an average of 11 minutes. Given that he/she has already waited 27 minutes after placing the order, and the food hasn't arrived yet, what is the probability that he/she ordered from Diner A? HINT: Use continuous probability distributions methods.
During a professor's office hours, students arrive, on average, every ten minutes. Assume that the distribution of the time between arrivals follows an exponential distribution. Suppose that a student has just left. Suppose that a student has just left. Only 25% of the time will the professor have to wait approximately how long or longer before the next student shows up?
DLP projectors are used in the majority of cinema projection systems and require a special light bulb to display a picture. Assume that the average life of a DLP bulb is 2,000 hours and that this failure time follows the exponential distribution. Answer the following questions, performing all computations with Excel functions.
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?
Suppose a group of consumers spend 30% of their disposable income on food, 20% on clothing, and 50% on rent. If over the course of a year the price of food rises 10%, the price of clothing drops 5% and rent rises 15%, what is the average price increase experienced by these consumers?
Airborne concentrations of a pollutant follow a lognormal distribution. The pollutant has concentrations that exceed 1.5 ppm 33% of the time, and exceed 6.025 ppm 2.5% of the time. What fraction of the time is 13.934 ppm exceeded?
Personal care aide is an occupation that is growing quickly. Assume that, in a certain region, there will be a need for 195,686 personal care aides in 2024, a growth of about 29% over 2014 levels. How many personal care aides were there in this region in 2014?
Intel co-founder Gordon Moore noticed that the number of transistors on integrated circuits had doubled approximately every two years since their invention. Moore's "law" predicted that this trend will continue into the foreseeable future. The Intel 4004 chip had 2,300 transistors in 1971. How many transistors should be possible in 2019? (Round to nearest billion) billion transistors