The time it takes a worker on an assembly line to complete a task isexponentially distributed with a mean of 8 minutes.[2] What is the probability density function for the time it takes tocomplete the task?10.а.[3] What is the probability that it will take a worker less than 4b.minutes to complete the task?[5] What is the probability that it will take a worker between 6 and 10minutes to complete the task?С.

Solution-: Given: Mean of exponential distribution =8 minutes We want to find (a) Probability…

Answered: The time it takes a worker on an…

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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Q1
The lifetime (in hours ) of a semiconductor laser has a lognormal distribution with theta = 10 and omega = 1.5 Determine the following in parts (a) and (b): a) Probability the lifetime is less than 1000 hours ? b) Probability the lifetime is less than 11000 hours given that it is more than 10000 hours?
The probability distribution of X, the number of imperfections for every 10 meters of a synthetic fabric in continuous rolls of uniform width, is given by 1 2 3 4 f(x) 0.41 0.37 0.17 0.05 0.01 find the mean and variance of X. (10 pts)
The distribution of the time until a Web site changes is important to Web crawlers that search engines use to maintain current information about Web sites. The distribution of the time until change (in days) of a Web site is approximated in the following table. Days until Probability Changes 1.5 0.05 0.25 0.35 0.20 0.15 3 4.5 7 Calculate the probability mass function of the days until change. *Answers should be in rational numbers with 2 decimal places.
11. Suppose random variable X is distributed as normal with mean 2 and standard deviation 3 and random variable Y with mean 0 and standard deviation 4, what is the probability density function (pdf) of X + Y.
Let Y be an exponential random variable with (unknown) mean 0.
The time to first failure X of the software of a medical linear acceleratormay be modeled normal with μ = 1100 hours and σ = 50 hours.
The level of nitrogen oxides (NOX) and nonmethane organic gas (NMOG) in the exhaust over the useful life (150,000150,000 miles of driving) of cars of a particular model varies Normally with mean 8080 mg/mi and standard deviation 66 mg/mi. A company has 1616 cars of this model in its fleet. Using Table A, find the level ?L such that the probability that the average NOX + NMOG level ?¯x¯ for the fleet greater than ?L is only 0.030.03 ? (Enter your answer rounded to three decimal places. If you are using CrunchIt, adjust the default precision under Preferences as necessary. See the instructional video on how to adjust precision settings.)
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 solid insulating specimens subjected to AC voltage. The values of the parameters depend on the voltage and temperature; suppose a = 2.6 and B = 220. (a) What is the probability that a specimen's lifetime is at most 250? Less than 250? More than 300? (Round your answers to five decimal places.) at most 250 less than 250 more than 300 0.7520 0.7520 0.1065 x X X (b) What is the probability that a specimen's lifetime is between 100 and 250? (Round your answer to four decimal places.) 0.6312 (c) What value (in hr) is such that exactly 50% of all specimens have lifetimes exceeding that value? (Round your answer to three decimal places.) 191 Xhr
The life X (in hours) of a battery in constant use is a random variable with exponential density. What is the probability that the battery will last more than 12 hours (h) if the average life is 8 h?
The probability that an event will not happen is PE′=0.79. Find the probability that the event will happen.

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