please just answer IV & V A large population (consisting of measurements of diameters of ball bearings) has mean uand standard deviation o, neither of which is perfectly known. A random sample of sizen = 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 variableswith u = E(U1) and Var(U1) = o². No further knowledge about the shape of the distributionis known. Define,251X 25Ui25i=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 ofP(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.

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

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ISBN:9781119256830

Author:Amos Gilat

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Chapter1: Starting With Matlab

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Question

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.

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