The Weibull distribution is widely used in statistical problems relating to aging of solid insulating materials subjected to aging and stress. Use this distribution as a model for time (in hours) to failure of solidinsulating specimens subjected to AC voltage. The values of the parameters depend on the voltage and temperature; suppose a = 2.6 and B = 190.(a) What is the probability that a specimen's lifetime is at most 250? Less than 250? More than 300? (Round your answers to four decimal places.)at most 250less than 250more than 300(b) What is the probability that a specimen's lifetime is between 100 and 250? (Round your answer to four decimal places.)(c) What value is such that exactly 50% of all specimens have lifetimes exceeding that value? (Round your answer to three decimal places.)hr

Given information α = 2.7 β = 210 a) i) The probability that a specimen's lifetime is at most 250 is…

Answered: The Weibull distribution is widely used…

MATLAB: An Introduction with Applications

6th Edition

ISBN:9781119256830

Author:Amos Gilat

Publisher:Amos Gilat

Chapter1: Starting With Matlab

Section: Chapter Questions

Problem 1P

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Question 6 Consider a queueing system where the customers' time between arrivals is exponentially distributed with an average rate of 2.1 customers per hour. The service time distribution is not known but the average is 7.8 customers per hour. If the standard deviation of the service time is 0.8 hours, what is the expected number of clients in the system? Add your answer
Question 2 (a) Let X - Uniform(0, 1) distribution. Find the PDF of Y = VX. (b) Derive the expected value and the variance of Y
Assuming a loss frequency of a loss occurring once every 2 years and that the average value of losses that occur might be $40,000. Based on the above examples the expected loss is
6. The magnitude (Richter scale) of earthquake along a Taiwanese fault is exponentially distributed, with A= (1/2.5). What is the probability of an earthquake exceeding magnitude 6.4? There is 1 earthquake per year (on average) along the fault with magnitude greater than 5.5. Given this, what is the probability of an earthquake during the year that exceeds magnitude 7.2?
Question 18
Read the question carefully and give me both a&b right solution according to the question. A catalyst powder has the following weight distribution in the given particle size range: 10-20 µm, 10.0 %; 20-30 µm, 42.0 %; 30-40 µm, 33.0 %; 40-50 µm. 9.0 %; 50-80 µm, 5.9 %. From a log-probability plot estimate (a) the geometric mean diameter, (b) the standard deviation of that mean diameter.
Sales delay is the elapsed time between the manufacture of a product and its sale. According an article it is quite common for investigators to model sales delay using a lognormal distribution. For a particular product, the cited article proposes this distribution with parameter values μ = 2.02 and o2 = 0.05 (here the unit for delay is months). USE SALT (a) What are the variance and standard deviation of delay time? (Round your answers to two decimal places.) months2 variance 3.06 standard deviation 1.75 ✔ months (b) What is the probability that delay time exceeds 12 months? (Round your answer to four decimal places.) 0.0188 (c) What is the probability that delay time is within one standard deviation of its mean value? (Round your answer to four decimal places.) 0.1024 x (d) What is the median of the delay time distribution? (Round your answer to two decimal places.) 7.54 months (e) What is the 99th percentile of the delay time distribution? (Round your answer to two decimal places.)…
Practice Question 3: Suppose the time to do a health check (X) is exponentially distributed with an average of 20 minutes. a) What is the parameter of this exponential distribution (2)? b) What is the probability that a health check can be done in less than 15 minutes? c) What is the probability that a health check can be done in more than 25 minutes? d) What is the probability that a health check can be done in between 15 and 25 minutes? e) A health check already took 20 minutes, what is the probability that the health check can be done in less than 30 minutes?
Sales delay is the elapsed time between the manufacture of a product and its sale. According an article it is quite common for investigators to model sales delay using a lognormal distribution. For a particular product, the cited article proposes this distribution with parameter values μ = 2.08 and o² = 0.03 (here the unit for delay is months). USE SALT (a) What are the variance and standard deviation of delay time? (Round your answers to two decimal places.) 2.01 1.42 ✓ months² months variance standard deviation (b) What is the probability that delay time exceeds 12 months? (Round your answer to four decimal places.) 0096 (c) What is the probability that delay time is within one standard deviation of its mean value? (Round your answer to four decimal places.) 0.8485 X (d) What is the median of the delay time distribution? (Round your answer to two decimal places.) 8.00 months (e) What is the 99th percentile of the delay time distribution? (Round your answer to two decimal places.)…
The lifetime T (in years) for a particular type of electric toothbrush is assumed to have the probability density f given by t 0 ≤ t ≤6 f(t) = {+ 3 18 otherwise.
Question 1 Let x be a continuous random variable that is normally distributed with a mean of 60 and astandard deviation of 9. Find the probability that x assumes a value between 55 to 75.
A person's blood glucose level and diabetes are closely related. Let x be a random variable measured in milligrams of glucose per deciliter (1/10 of a liter) of blood. Suppose that after a 12-hour fast, the random variable x will have a distribution that is approximately normal with mean μ = 86 and standard deviation o = 23. Note: After 50 years of age, both the mean and standard deviation tend to increase. For an adult (under 50) after a 12-hour fast, find the following probabilities. (Round your answers to four decimal places.) USE SALT (a) x is more than 60 1292 (b) x is less than 110 0.9236 X (c) x is between 60 and 110 0.7526 (d) x is greater than 125 (borderline diabetes starts at 125) 6.3

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