(c) A group of scientists is measuring an unknown quantity u ER by repeating independent experiments. Let X be the value measured by the k-th experiment. If the experiment is repeated for n times, the approximated value of μ, is given by the sample mean Xn = X₁ + ... + Xn n fl (The actual quantity is the (common) expected value of Xk.) They have a strong evidence that each X has an approximated standard deviation o=3. Use central limit theorem to estimate how many experiments to repeat in order to be 98% sure that the approximated mean is within 0.1 margin of error from the actual value u?

A First Course in Probability (10th Edition)
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Chapter1: Combinatorial Analysis
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A group of scientists is measuring an unknown quantity μER by repeating
independent experiments. Let X be the value measured by the k-th experiment. If
the experiment is repeated for n times, the approximated value of μ, is given by the
sample mean
Xn
=
X₁ + ... + Xn
N
(The actual quantity is the (common) expected value of Xk.) They have a strong
evidence that each X has an approximated standard deviation o= 3. Use central
limit theorem to estimate how many experiments to repeat in order to be 98% sure
that the approximated mean Xn is within 0.1 margin of error from the actual value
fe?
Transcribed Image Text:A group of scientists is measuring an unknown quantity μER by repeating independent experiments. Let X be the value measured by the k-th experiment. If the experiment is repeated for n times, the approximated value of μ, is given by the sample mean Xn = X₁ + ... + Xn N (The actual quantity is the (common) expected value of Xk.) They have a strong evidence that each X has an approximated standard deviation o= 3. Use central limit theorem to estimate how many experiments to repeat in order to be 98% sure that the approximated mean Xn is within 0.1 margin of error from the actual value fe?
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