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A large population (consisting of measurements of diameters of ball bearings) has mean u and standard deviation o, neither of which is perfectly known. A random sample of size n = 25 observations will be taken, namely the diameters U1, U2, · , U25 will be observed. In other words, U1, U2, · · · , U25 are independent and identically distributed random variables with u = E(U1) and Var(U1) =o². No further knowledge about the shape of the distribution is known. Define, .. X» = u. 25 1 25

A large population (consisting of measurements of diameters of ball bearings) has mean u and standard deviation o, neither of which is perfectly known. A random sample of size n = 25 observations will be taken, namely the diameters U1, U2, · , U25 will be observed. In other words, U1, U2, · · · , U25 are independent and identically distributed random variables with u = E(U1) and Var(U1) =o². No further knowledge about the shape of the distribution is known. Define, .. X» = u. 25 1 25

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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please just answer IV & V

A large population (consisting of measurements of diameters of ball bearings) has mean u and standard deviation o, neither of which is perfectly known. A random sample of size n = 25 observations will be taken, namely the diameters U1, U2, ·.., U25 will be observed. In other words, U1, U2, · .., U25 are independent and identically distributed random variables with u = E(U1) and Var(U1) = o². No further knowledge about the shape of the distribution is known. Define, 25 1 X 25 Ui 25 i=D1 (i) If someone says E(X 25) = 13, what information does he give you about u, if any? (ii) If someone says o = 5, what is Var(X25)? • (iii) What is the chance, approximately, that a sample of size n = 25 will have its mean, X25, smaller than the population mean u? In other words, find an approximation of P(X 25 < u). [Hint: see if the value of o is relevant or not to answer the question.] (iv) In part (iii) while approximating what theorem did you use, if any? • (v) What is the chance, approximately, that a sample of size n = 25 will have its mean, X25, smaller than u+ 1, when o = 1.
Transcribed Image Text:A large population (consisting of measurements of diameters of ball bearings) has mean u and standard deviation o, neither of which is perfectly known. A random sample of size n = 25 observations will be taken, namely the diameters U1, U2, ·.., U25 will be observed. In other words, U1, U2, · .., U25 are independent and identically distributed random variables with u = E(U1) and Var(U1) = o². No further knowledge about the shape of the distribution is known. Define, 25 1 X 25 Ui 25 i=D1 (i) If someone says E(X 25) = 13, what information does he give you about u, if any? (ii) If someone says o = 5, what is Var(X25)? • (iii) What is the chance, approximately, that a sample of size n = 25 will have its mean, X25, smaller than the population mean u? In other words, find an approximation of P(X 25 < u). [Hint: see if the value of o is relevant or not to answer the question.] (iv) In part (iii) while approximating what theorem did you use, if any? • (v) What is the chance, approximately, that a sample of size n = 25 will have its mean, X25, smaller than u+ 1, when o = 1.
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