The lifetime of a washing machine (in days) is known to have a Gamma distribution with...
The lifetime of a washing machine (in days) is known to have a Gamma distribution with shape parameter equal to 1 and scale parameter equal to 14.1.
Find the probability that the machine works for more than 19 days before it breaks. Round your answer to three digits.
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The lifetime of a washing machine (in days) is known to have a
Gamma distribution with...
The usable lifetime of a particular electronic component is known to follow an exponential distribution with...
The usable lifetime of a particular electronic component is known to follow an exponential distribution with a mean of 6.6 years. Let X = the usable lifetime of a randomly selected component. (a) The proportion of these components that have a usable lifetime between 5.9 and 8.1 years is . (b) The probability that a randomly selected component will have a usable life more than 7.5 years is . (c) The variance of X is
2. Light bulbs are known to have an average lifetime of 2,000 hours. Suppose we model...
2. Light bulbs are known to have an average lifetime of 2,000 hours. Suppose we model the lifetime of a light bulb by the following probability density function with (yet unknown) parameter c: p(t) = 1-e-t/c when t20 and p(t) = 0 otherwise. (a) Determine the value of the parameter c so that the probability density function has mean 2,000 hours. (b) Determine the probability a lightbulb fails before 1,500 hours. (C) Suppose the lightbulb has already been on for...
The Quick Wash 24-hour Laundromat has 16 washing machines. A machine breaks down every 20 days...
The Quick Wash 24-hour Laundromat has 16 washing machines. A machine breaks down every 20 days (exponentially distributed). The repair service with which the Laundromat contracts takes an average of 1 day to repair a machine (exponentially distributed). A washing machine averages $5 per hour in revenue. The Laundromat is considering a new repair service that guarantees repairs in 0.50 day, but it charges $10 more per hour than the current repair service. Should the Laundromat switch to the new...
Problem 4 (12 points; 2,2|414) Consider a certain machine part. Let X = lifetime (in days)...
Problem 4 (12 points; 2,2|414) Consider a certain machine part. Let X = lifetime (in days) of the machine part Suppose that pdf of the random variable X is given by: 4 xexp -x2 otherwise 4pts The random variable X is said to have a Weibull distribution with parameters " and β ' On average, how many days does the machine part last? E(X)- 4pts 4pts Find the probability the machine part survives over 25 days? P(X> 25)-
Your job is to make sure that a washing machine lasts more than 10 years, the...
Your job is to make sure that a washing machine lasts more than 10 years, the warranty period, with probability 0.99. As it is, the mean lifetime is 10 years with standard deviation 2.5 years, and it is Gaussian distributed. You can leave the standard deviation the same for no cost. To reduce the standard deviation, it costs $100 to reduce the standard deviation to 1.5 years, or $200 to reduce it to 0.5 years. It costs $50 per year...
The number of visits to a website is known to have a Poisson distribution with a...
The number of visits to a website is known to have a Poisson distribution with a mean of 10 visits per minute. a) What is the probability distribution for x, the number of visits per minute? p(X)=?? b) What is the probability that the number of visits per minute is less than or equal to 10? (Round your answer to three decimal places.) c) What is the probability that the number of visits per minute is greater than 14? (Round...
The operating lifetime of an electronic component is known to have a normal distribution with mean...
The operating lifetime of an electronic component is known to have a normal distribution with mean of 2,500 hours and variance of 40,000 (hours^2). Given that the component has been operating for 2,350 hours, what is the probability that it will still be operating beyond 2,750 hours?
The life time of a particular brand smartphone's battery is known to have Gamma distribution with...
The life time of a particular brand smartphone's battery is known to have Gamma distribution with αα = 4 and ββ = 2. If we take a random sample of 50 these batteries, what is the probability that the average life time of this random sample will be between 7 and 9 months?
The lifetime of an electronic component, L, is known to have a variance of 72 (hours2)...
The lifetime of an electronic component, L, is known to have a variance of 72 (hours2) (a) Using Chebyshev's Inequality, find a lower bound on the probability that the lifetimes are within 20 hours of the mean (b) Suppose it is found that the lifetimes actually follow an exponential distribution Determine the eract probability that the lifetimes are within 20 hours of the mean
The lifetime of traditional light bulbs measured in hours is known to be normally distributed with...
The lifetime of traditional light bulbs measured in hours is known to be normally distributed with μ=100 and σ=20. What is the probability that a randomly selected traditional light bulb will have a lifetime of 125 hours or longer? You need to use a normal distribution table. Find the nearest answer. a. 4.006% b. 22.663% c. 10.565% d. 77.337% e. 89.435%
2. Light bulbs are known to have an average lifetime of 2,000 hours. Suppose we model the lifetime of a light bulb by the following probability density function with (yet unknown) parameter c: p(t) = 1-e-t/c when t20 and p(t) = 0 otherwise. (a) Determine the value of the parameter c so that the probability density function has mean 2,000 hours. (b) Determine the probability a lightbulb fails before 1,500 hours. (C) Suppose the lightbulb has already been on for...
Problem 4 (12 points; 2,2|414) Consider a certain machine part. Let X = lifetime (in days) of the machine part Suppose that pdf of the random variable X is given by: 4 xexp -x2 otherwise 4pts The random variable X is said to have a Weibull distribution with parameters " and β ' On average, how many days does the machine part last? E(X)- 4pts 4pts Find the probability the machine part survives over 25 days? P(X> 25)-
The lifetime of an electronic component, L, is known to have a variance of 72 (hours2) (a) Using Chebyshev's Inequality, find a lower bound on the probability that the lifetimes are within 20 hours of the mean (b) Suppose it is found that the lifetimes actually follow an exponential distribution Determine the eract probability that the lifetimes are within 20 hours of the mean
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