A steel manufacturer is testing a new additive for manufacturing an alloy of steel. The jointprobability mass function of tensile strength (in thousands of pounds/in?) and additiveconcentration isTensile StrengthConcentration of Additive1001502000.110.020.050.060.040.010.080.100.170.060.040.080.080.040.140.12What are the marginal probability mass functions for X (additive concentration) and Y(tensile strength)?Are X and Y independent? Explain.a.b.Given that a specimen has an additive concentration of 0.04, what is the probabilitythat its strength is 150 or more?Given that a specimen has an additive concentration of 0.08, what is the probabilitythat its tensile strength is greater than 125?A certain application calls for the tensile strength to be 175 or more. What additiveconcentration should be used to make the probability of meeting this specification thegreatest?C.d.e.

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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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The number of mole of toluene in each independent sample of water from a certain river follows a distribution with the following probability density function 5e- f(x) = -5x x 20 otherwise Find the probability that a collection of 50 such samples will have an average value (a) less than 0.2 mole; (b) between 0.18 and 0.205 mole. You can leave your answer in terms of ¤, the CDF of standard normal distribution. Hint: use the Central Limit Theorem.
The lifetime X of a widget has a Weibull distribution with parameters a = 2 and B = 5. The mean widget lifetime is E[X] = 4.43. The standard deviation of the lifetime is StDev(X) = 2.316. What is the probability the widget lasts between 2.6 and 5.2? P( 2.6 < X < 5.2 ) = Express your answer as a proportion rounded to 4 decimal places.
A continuous random variable X has a pdf of the form: f(x) = (620/801) x^3, for 0.42< X<1.51. Calculate the standard deviation (sigma) of X. Your answer: 0.277 O 0.679 0.320 0.444 0.999 0.731 O 0.238 0.822 O 0.383 0.268
-3 -2 -1 0 1 2 3 Please show your answer to 2 decimal places. About % of the area under the curve of the standard normal distribution (µ = 0 and o = 1) is outside the interval Z = (-0.74,0.74) (or beyond 0.74 standard deviations of the mean).
Young's modulus is a quantitative measure of stiffness of an elastic material. Suppose that for metal sheets of a particular type, its mean value and standard deviation are 70 GPa and 2.4 GPa, respectively. Suppose the distribution is normal. (Round your answers to four decimal places.) A USE SALT (a) Calculate P(69 sīs 71) when n = 16. (b) How likely is it that the sample mean diameter exceeds 71 when n = 36? You may need to use the appropriate table in the Appendix of Tables to answer this question.
Let x be the amount of time (in minutes) that a particular San Francisco commuter must wait for a train. Suppose that the density curve is as pictured below (a uniform distribution). Density 0.05 0 Time (minutes) (a) What is the probability that x is less than 11 min? What is the probability that x is more than 17 min? I 20 (b) What is the probability that x is between 8 and 14 min? (c) Find the value c (in minutes) for which P(x < c) = 0.7. C = min X
show all solution A wine’s distinctive taste is a result of ageing it in wooden casks. Some of the wine evaporates while it is aging in the porous wooden casks. Define X=percentage of wine in the cask that is lost due to evaporation. Suppose X is normally distributed with mean 5% and a standard deviation of 1%. What is the probability of losing more than 7.5% of the wine due to evaporation?
Porosity measurements for several reservoir formations have been accomplished. The results imply that probability density function of the measurements is constant at a value of o.25. The used measurements in this study have porosity values from 4% to 8%. Determine the proportion of the measurements thathave 7%-8% porosity.
(2) JAL ?Q13) Consider the following probability density function, what is the F(14) 0.22 X= 7 0.22 0.05 0.05 0.06 X = 9 X= 11 f (x) X = 13 15 0.33 X = 17 0.06 0.01 X = 19 X = 23 0.54 0.6 0.93 0.99 EN LG
Young's modulus is a quantitative measure of stiffness of an elastic material. Suppose that for metal sheets of a particular type, its mean value and standard deviation are 75 GPa and 2.3 GPa, respectively. Suppose the distribution is normal. (Round your answers to four decimal places.) n USE SALT (a) Calculate P(74 sis 76) when n = 16. (b) How likely is it that the sample mean diameter exceeds 76 when n = 36? You may need to use the appropriate table in the Appendix of Tables to answer this question.
-3 -2 -1 0 1 2 3 Please show your answer to 2 decimal places. About % of the area under the curve of the standard normal distribution (u = 0 and o = 1) is outside the interval Z = (-1.02,1.02) (or beyond 1.02 standard deviations of the mean).
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