Our department seminar room is lit by 7 light bulbs, controlled by a single switch. A minimum of 3 lights are needed for the room to be usable. Suppose the lifetime of the brand of light bulbs fitted is exponentially distributed with a mean of 400 hours. Assume a seminar lasts exactly 1 hour, and that the lights are switched on only during the seminar. What is the probability that after 500 seminars, exactly 3 bulbs do not need to be replaced? You may need to use a calculator. Give your answer rounded to 4 decimal places. Answer:

Our department seminar room is lit by 7 light bulbs, controlled by a single switch. A minimum of 3 lights are needed for the room to be usable. Suppose the lifetime of the brand of light bulbs fitted is exponentially distributed with a mean of 400 hours. Assume a seminar lasts exactly 1 hour, and that the lights are switched on only during the seminar. What is the probability that after 500 seminars, exactly 3 bulbs do not need to be replaced? You may need to use a calculator. Give your answer rounded to 4 decimal places. Answer:

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

Related questions

Q: The amount of time spouses shop for anniversary cards can be modeled by an exponential distribution…

Q: The time between arrivals of buses at a bus stand is exponentially distributed with a mean of 20…

A: Problem can be solved using exponential distribution formula.

Q: ou are waiting in line at Dunkin. There are three people in front of you. The time it takes a person…

Q: The life of a power transmission tower is exponentiallydistributed, with mean life 25 years. If…

A: From the given information, it can be observed that the life of a power transmission tower is…

Q: A company sells laptops with a warranty of 2 years. The probability of a laptop failing during the…

A: Here given that a company sells laptops with a warranty of 2 years. The probability of a laptop…

Q: person who goes home from work has the opportunity to choose one of two ways. Their probability of…

Q: If each day there's a 60 percent chance Joe will eat lunch, what is the probability that he'll eat…

A: Given: Each day there is 60% chance Joe will eat lunch. Objective of the question is to calculate…

Q: 84% of all the field goals he kicks during in-season games. Assume each kick is independent of the…

A: Let X be the random variable from binomial with probability (p) = 84% = 0.84 and sample size (n) =…

Q: The life of a power transmission tower is exponentially distributed, with mean life 25 years. If…

Q: lobe has a number of inquiries arriving in their system at 3 inquiries per minute. What is the…

A: Consider X denotes inquiries arriving in the system which follows Poisson distribution with λ=3.

Q: the time between the arrival of the passengers at the airport follows exponential with a mean of 12…

A: given data time between arrival = 12 minutesλ = 112 per minutex = no. of arrival in t minutest = 15…

Q: A technology manufacturing company has recently switched to the production of isolinear processors.…

Q: Ahmed, Omar and Salem have applied for the nomination to be the chairman of the student council at…

A: Given that there are three persons Ahmad, Omar and Salem have applied for the nomination to be the…

Q: The length of time a person shops for groceries can be modeled by an exponential distribution with…

A: It is given that the time a person shops for groceries is exponential distributed with mean 27 min.

Q: In China approximately 70% of people are either vaccinated or have immunization from a previous…

A: Let us define the following events: E1: A person is vaccinatedE2: A person is not vaccinated…

Q: It is known that the shelf life of refills for a certain brand of purifier of water is exponentially…

A: Exponential Distribution: A continuous random variable X is said to follow Exponential distribution…

Q: The number of days ahead travelers purchase their airline tickets can be modeled by an exponential…

A: The question is about exponential distribution.Given :No. of days travelers wait to purchase a…

Q: Doctors have indicated that 33% of the US population has A+ blood which is the second most common…

Q: Industrial robots are programmed to operate through microprocessors. The probability that one such…

A: The objective of the question is to find the probability that the robot will operate for at most 5…

Q: The frequency of twin births has been increasing in recent years so that in 2022 about 4% of all…

A: From given in 2022 about 4% of all births were twins. and The probability of a birth being that of…

Q: A landscaper mows 25 lawns per day on sunny days, 15 lawns per day on cloudy days, and no lawns if…

Q: if a seed is planted, it has a 65% chance of growing into a healthy plant. if 6 seeds are planted,…

Q: 4. A fire detection device uses 3 temperature-sensitive cells acting independently of each other in…

A: (4)

Q: The magnitudes of earthquakes recorded in a region of North America can be modeled by an exponential…

Q: A drug test correctly gives a positive result 90 percent of the time. However, 3 percent of the…

Q: A toy factory produces battery operated toy robots for toddlers. Previous research shows that the…

A: It is given that the lifetime of robots (say X) is exponentially distributed with a mean of 6…

Q: Suppose that on the average, 7 students enrolled in a small liberal arts college have their…

A: Let X=no.of enrolled in a small liberal arts college have their automobiles stolen during the…

Question

Transcribed Image Text:Our department seminar room is lit by 7 light bulbs, controlled by a single switch. A minimum of 3 lights are needed for the room to be usable. Suppose the lifetime of the brand of light bulbs fitted is exponentially distributed with a mean of 400 hours. Assume a seminar lasts exactly 1 hour, and that the lights are switched on only during the seminar. What is the probability that after 500 seminars, exactly 3 bulbs do not need to be replaced? You may need to use a calculator. Give your answer rounded to 4 decimal places. Answer:

Expert Solution

This question has been solved!

Explore an expertly crafted, step-by-step solution for a thorough understanding of key concepts.

SEE SOLUTION Check out a sample Q&A here

Step 1

Step 2

Step 3

Step 4

Step 5

Step 6

Step by step

Solved in 6 steps with 6 images

SEE SOLUTION Check out a sample Q&A here

Similar questions

A hacker breaking into a computer system has a 15% chance of breaking into a system in 2 minutes, a 25% chance after 5 minutes, and a 60% chance after 20 minutes. What is the expected time will take the hacker to get in?
If the probability of hitting a goal ball player is 0.4, then if this player wants to hit the goal seven times until he stops, what is the probability that he achieves that from 10 shots?
The amount of time spouses shop for anniversary cards can be modeled by an exponential distribution with the average amount of time equal to 58 minutes. What is the probability that a randomly selected spouse spends no more than 20 minutes shopping for an anniversary card?
Imagine an animal that shows two variants; one long-legged and one short-legged. Each female produces 2 female offspring per generation and then dies. The offspring of the long-legged ones survive to adulthood (reproductive age) with a probability of 55% and the offspring of the short-legged ones survive to adulthood with a probability of 45%. If you begin with a population of 60 females of each type, what proportion of individuals will have long legs in 5 generations? (Note that you can ignore males and count only females and their offspring.) Show all work.
6. On the average, it takes 25 seconds to download a file from the internet. If it takes an exponential amount of time to download one file, then what is the probability that it will take more than 70 seconds to download 3 independent files?
The delivery time of a shipment from a supplier to a retailer is exponentially distributed with mean 7 days. The supplier must deliver a shipment by 14 days. What is the probability that shipment takes more than 14 days? Show your work.
The mosquitos are out in your back yard, and they bite you at random times. Each bite happens independently of the last bite. The average time between bites is 2.501 minutes. What is the probability that it takes longer than 1 minutes for them to first bite you?
The amount of time spouses shop for anniversary cards can be modeled by an exponential distribution with the average amount of time equal to 42 minutes. What is the probability that a randomly selected spouse spends more than 12 but less than 104 minutes to shop for an anniversary card?
For any day in July, there is a 20% chance of rainfall. An engineering construction company plans to cast a slabthat requires no rainfall during its casting period extending over 5 days. What is the probability of having no rainfallduring the casting period and one rainy day during the casting period?