The time to failure (in hours) for a laser in a cytometry machine is modeled by an exponential distribution withthe answers to 3 decimal places.(a) What is the probability that the laser will last at least 20675 hours?(b) What is the probability that the laser will last at most 30974 hours? i(c) What is the probability that the laser will last between 20675 and 30974 hours? *= 0.00004. Round

Answered: The time to failure (in hours) for a…

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...

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The time it takes to travel from my apartment to work is normally distributed with μ = 25 minutes and σ = 5 minutes. What is the probability that my commute time tomorrow will take between 30 and 35 minutes?(please round your answer to 2 decimal places)
Suppose X has an exponential distribution with mean equal to 12. Determine the following: (a) P(X > 10) (Round your answer to 3 decimal places.) (b) P(X > 20) (Round your answer to 3 decimal places.) (c) P(X < 30) (Round your answer to 3 decimal places.) (d) Find the value of x such that P(X
Consider an electronic component with a lifetime denoted by a random variable T which is modelled by an exponential distribution with a parameter of average lifetime B = 5. Part A: Exponential Distribution Write the probability that a component is still working after 5 years, as an expression: P(T > 5) = | dt Use t for T e() for exponential function ()! for factorial ( )*( ) for exponents • Help entering equations Part B: Probability Write the probability that a component is still working after 5 years, numerically: P(T > 5) = • Help entering equations Part C: Binomial Distribution Let X be the random variable representing the number of components that are still working after 5 years. Write the binomial distribution for at least 3 components that are still working, as an expression: P(X 2 3) = Use p for parameter p x for the value of the random variable X e() for exponential function C(n,x) for combination of "x out of n" (O! for factorial (O*) for exponents • Help entering equations…
The time intervals between successive barges passing a certain point on a busy waterway have an exponential distribution with mean 10 minutes. (a) Find the probability that the time interval between two successive barges is more than 15 minutes. (b) Find a time interval t such that we can be 75% sure that the time interval between two successive barges will be greater than t. Show word count Next
Please solve (a) & (b) only!
2 The operator of a pumping station has observed that demand for water during early afternoon hours has an approximately exponential distribution with mean 100 cfs (cubic feet per second). (a) Find the probability that the demand will exceed 250 cfs during the early afternoon on a randomly selected day. (Round your answer to four decimal places.) (b) What water-pumping capacity, in cubic feet per second, should the station maintain during early afternoons so that the probability that demand will exceed capacity on a randomly selected day is only 0.02? (Round your answer to two decimal places.) cfs
The time between failures of our video streaming service follows an exponential distribution with a mean of 40 days. Our servers have been running for 17 days, What is the probability that they will run for at least 97 days? (clarification: run for at least another 80 days given that they have been running 17 days). Report your answer to 3 decimal places.
The lifetime of a specific species of mammal is normally distributed with mean μ=22 years and standard deviation σ=4 years. We pick randomly a mammal from the above species. What is the probability the mammal lives: Less than 28years? Between 20 years and 28 years? Exactly 67% of the mammal of this species live at most y What is the value of y?
Q life time of led follow exponential distribution with mean life of 5000 burning hours. if one such LED is selected at random from a big lot, what is the probability that it will last for 1. at least 4000 hours 2. almost 10000 hours Also state the standard deviation of the life time distribution. Given e raised to -0.8 is 0.4493 and e raised to -2 is 0.1353
local gym has only one treadmill machine for cardio exercises. Suppose exponential interarrival times with mean of 2 per hour, and exponential usage times with mean of 30 minutes per customer. Suppose a person has just arrived at 12.00 noon to use Assume your the machine. What is the probability that the next arrival will come before 1.00 pm, between and after 2.00 pm? Note that you have to provide three 1.00 pm and 2.00 pm, answers, one for each. Suppose no customer arrives before 1.00 pm. What is the probability that the next arrival will come between 1.00 pm and 2.00 pm? What is the probability that the number of arrivals between 1.00 pm and 2.00 pm will be zero (one, more than one)?
If I had a series of data X = (x₁+x₂+x₂+ 1 2 +xN} I would have a mean and standard deviation, and s X If I subtracted 3 from every observation in the data series, X, which of the following would happen? The mean of X will increase by 3 The mean of X will decrease by 3 The standard deviation of X will be three times as large The standard deviation of X will be one third as large 3 ...

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