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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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.](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2Fbcac37ab-99fb-4492-b15f-6751da0b26b9%2F10f566c2-3bc1-45e5-a4f4-872ab7e4faf4%2Fkiyee9r_processed.png&w=3840&q=75)
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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