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A synthetic fiber used in manufacturing carpet has tensile strength (in psi) following gamma distribution with a 1 and λ = 0.1. Find the probability that a random sample of n = 10 fiber specimens will have sample 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 the sample mean exceeds 10.5 psi? (b) Using the central n limit theorem, we have x ~AN(, α -). What is the λ 2 λη probability 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) with n = 1J0 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 (in psi) following gamma distribution with a 1 and λ = 0.1. Find the probability that a random sample of n = 10 fiber specimens will have sample 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 the sample mean exceeds 10.5 psi? (b) Using the central n limit theorem, we have x ~AN(, α -). What is the λ 2 λη probability 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) with n = 1J0 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?

MATLAB: An Introduction with Applications
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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A synthetic fiber used in manufacturing carpet has tensile strength (in psi) following gamma distribution with a 1 and λ = 0.1. Find the probability that a random sample of n = 10 fiber specimens will have sample 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 the n sample mean exceeds 10.5 psi? (b) Using the central α limit theorem, we have x -AN( ~, x). What is the 2 λ λη probability 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) with 10? 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?
Transcribed Image Text:A synthetic fiber used in manufacturing carpet has tensile strength (in psi) following gamma distribution with a 1 and λ = 0.1. Find the probability that a random sample of n = 10 fiber specimens will have sample 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 the n sample mean exceeds 10.5 psi? (b) Using the central α limit theorem, we have x -AN( ~, x). What is the 2 λ λη probability 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) with 10? 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?
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