A large population (consisting of measurements of diameters of ball bearings) has mean µ 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, · · · , U2, are independent and identically distributed random variables with µ = E(U1) and Var(U1) = o². No further knowledge about the shape of the distribution is known. Define, 25 (i) If someone says E(X25) = 13, what information does he give you about µ, if any? %3D (ii) If someone says o = 5, what is Var(X23,)? • (iii) What is the chance, approximately, that a sample of size n = 25 will have its mean, X25, smaller than the population mean µ? In other words, find an approximation of P(X25 < 4). [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 µ + 2, when ở = 5. • (vi) From a sample of size n = 25 find an approximate value of P(µ – 2
A large population (consisting of measurements of diameters of ball bearings) has mean µ 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, · · · , U2, are independent and identically distributed random variables with µ = E(U1) and Var(U1) = o². No further knowledge about the shape of the distribution is known. Define, 25 (i) If someone says E(X25) = 13, what information does he give you about µ, if any? %3D (ii) If someone says o = 5, what is Var(X23,)? • (iii) What is the chance, approximately, that a sample of size n = 25 will have its mean, X25, smaller than the population mean µ? In other words, find an approximation of P(X25 < 4). [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 µ + 2, when ở = 5. • (vi) From a sample of size n = 25 find an approximate value of P(µ – 2
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Please Answer part (iv), (v) and (vi)
![6. A large population (consisting of measurements of diameters of ball bearings) has mean µ
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, ...,U2, 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
T25
• (i) If someone says E(X25) = 13, what information does he give you about µ, 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 µ? In other words, find an approximation of
P(X25 < H). [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 µ + 2, when o = 5.
(vi) From a sample of size n = 25 find an approximate value of P(µ – 2< X, <µ+2),
when σ- 10.](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2F421db798-cca4-4efb-a6a9-3775d86708c7%2F6b9134f4-2d61-44f8-8d6f-3f3399c73b04%2F9mge64a_processed.png&w=3840&q=75)
Transcribed Image Text:6. A large population (consisting of measurements of diameters of ball bearings) has mean µ
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, ...,U2, 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
T25
• (i) If someone says E(X25) = 13, what information does he give you about µ, 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 µ? In other words, find an approximation of
P(X25 < H). [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 µ + 2, when o = 5.
(vi) From a sample of size n = 25 find an approximate value of P(µ – 2< X, <µ+2),
when σ- 10.
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