A synthetic fiber used in manufacturing carpet hastensile strength (in psi) following gamma distributionwith a 1 and λ = 0.1. Find the probability that arandom sample of n = 10 fiber specimens will havesample mean tensile strength that exceeds 10.5 psi. (a)Recall the exact distribution on P. 16 of Chapter 7 note,we have x ~(na,nλ). What is the probability that thensample mean exceeds 10.5 psi? (b) Using the centralαlimit theorem, we have x -AN( ~, x). What is the2λληprobability that the sample mean - exceeds 10.5 psi? (c)Are the results in (a) and (b) similar? Which one is more"reliable" when = 10 ? (d) Repeat (a) and (b) with10?n 1 JO ar the esults similar?(c) Are the results in (a) and (b) similar? Which one is more "reliable"when n=10?(d) Repeat (a) and (b) with n = 1000, are the results similar?

A synthetic fiber used in manufacturing carpet has tensile strength following gammadistribution with…

Answered: A synthetic fiber used in manufacturing…

MATLAB: An Introduction with Applications

6th Edition

ISBN:9781119256830

Author:Amos Gilat

Publisher:Amos Gilat

Chapter1: Starting With Matlab

Section: Chapter Questions

Problem 1P

See similar textbooks

Similar questions

The compressive strength of concrete is normally distributed with mean 2500 psi and standard 50 psi. Find the probability that a random sample of n=5 specimens will have a sample mean diameter that falls in the interval from 2499 psi to 2510 psi. Answers in 4 significant figures.
A mixture of pulverized fuel ash and Portland cement to be used for grouting should have a compressive strength of more than 1,300 KN/m2. The mixture will not be used unless experimental evidence indicates conclusively that the strength specification has been met. Suppose compressive strength for specimens of this mixture is normally distributed with σ = 61. Let μ denote the true average compressive strength. For a test with α = 0.01, what is the probability that the mixture will be judged unsatisfactory when in fact μ = 1,350 (a type II error)? (Round your answer to four decimal places.)
The capacitance of capacitors produced by a machine is approximately normally distributed with a mean of µ = 1000 µF and a standard deviation of 80 µF. A sample of 16 capacitors is taken and the average of the capacitances values is computed. Based from the manufacturer’s standards, the machine is working properly if the computed average capacitance falls within 950 µF and 1050 µF. Otherwise, we conclude that µ ≠ 1000 µF. a.) Determine the probability of committing a type I error when µ = 1000 µF.b.) Determine the probability of committing a type II error when µ = 1080 µF. Hint: Use the sampling distribution of the mean when computing the probabilities
The weight of breads prepared in a baker is randomly distributed with a mean of 400 grams and standarddeviation of 16 grams. Using an independently selected sample of 16 breads,finda) the mean and standard deviation of the average weight of these 16 samples.b) using central limit theorem, estimate the probability that the average weight of samples is less than390.
The capacitance of capacitors produced by a machine is approximately normally distributed with a mean of ? =1000 μF and a standard deviation of 80 μF. A sample of 16 capacitors is taken and the average of the capacitancesvalues is computed. Based from the manufacturer’s standards, the machine is working properly if the computed average capacitance falls within 950 μF and 1050 μF. Otherwise, we conclude that ? ≠ 1000 μF.A. Determine the probability of committing a type I error when ? = 1000 μF.B. Determine the probability of committing a type II error when ? = 1080 μF.Hint: Use the sampling distribution of the mean when computing the probabilities.
The total energy needed during pregnancy is normally distributed, with a mean of 2600 kcal/ day and a standard deviation of 50 kcal/day. What is the probability that a random sample of 20 pregnant women has a mean energy need between 2575 and 2618?
The length of time, in seconds, that a computer user takes to read his or her email is distributed as a lognormal random variable with mean (theta) = 1.8 and variance (omega squared) = 4.0. 1) Determine the probability that the user reads the mail for more than 20 seconds.2) Determine the probability that the user reads the mail for a length of time that is equal to the mean of the underlying lognormal distribution?
A fishing line manufacturer tests the breaking stain of his products. He has found that, for a particular ‘line weight’, the maximum breaking stain follows a normal distribution, with a mean of 21.5kg and a standard deviation of 1.5kg. If a line is selected at random, calculate the probability that it has a breaking strain of between 22kg and 23.5kg.

Recommended textbooks for you

MATLAB: An Introduction with Applications

Statistics

ISBN:

9781119256830

Author:

Amos Gilat

Publisher:

John Wiley & Sons Inc

Probability and Statistics for Engineering and th…

Statistics

ISBN:

9781305251809

Author:

Jay L. Devore

Publisher:

Cengage Learning

Statistics for The Behavioral Sciences (MindTap C…

Statistics

ISBN:

9781305504912

Author:

Frederick J Gravetter, Larry B. Wallnau

Publisher:

Cengage Learning

MATLAB: An Introduction with Applications

Statistics

ISBN:

9781119256830

Author:

Amos Gilat

Publisher:

John Wiley & Sons Inc

Probability and Statistics for Engineering and th…

Statistics

ISBN:

9781305251809

Author:

Jay L. Devore

Publisher:

Cengage Learning

Statistics for The Behavioral Sciences (MindTap C…

Statistics

ISBN:

9781305504912

Author:

Frederick J Gravetter, Larry B. Wallnau

Publisher:

Cengage Learning

Elementary Statistics: Picturing the World (7th E…

Statistics

ISBN:

9780134683416

Author:

Ron Larson, Betsy Farber

Publisher:

PEARSON

The Basic Practice of Statistics

Statistics

ISBN:

9781319042578

Author:

David S. Moore, William I. Notz, Michael A. Fligner

Publisher:

W. H. Freeman

Introduction to the Practice of Statistics

Statistics

ISBN:

9781319013387

Author:

David S. Moore, George P. McCabe, Bruce A. Craig

Publisher:

W. H. Freeman

SEE MORE TEXTBOOKS