"The central limit theorem states that if X1, X2, X, are independent and identically .... distributed random variables, each having mean u and variance o?, then the distribution of X; tends to a normal distribution with mean u and variance o?." The statement above is erroneous. Point out the incorrect parts and ex plain why they are incorrect. It is known that the mean weight u of packages of a certain brand of supplement pills is 5.02 grams. Find the probability that a random sample of 100 such packages will have a mean weight between 4.96 and 5.00 grams. Assume that the standard deviation o is 0.30 grams. Leave your answer in 4 decimal places.

A First Course in Probability (10th Edition)
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ISBN:9780134753119
Author:Sheldon Ross
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Chapter1: Combinatorial Analysis
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Question 5
(a) "The central limit theorem states that if X1, X2, ... X, are independent and identically
distributed random variables, each having mean u and variance o?, then the distribution of
X; tends to a normal distribution with mean u and variance o?."
The statement above is erroneous. Point out the incorrect parts and explain why they are
incorrect.
(b) It is known that the mean weight u of packages of a certain brand of supplement pills is
5.02 grams. Find the probability that a random sample of 100 such packages will have a
mean weight between 4.96 and 5.00 grams. Assume that the standard deviation o is 0.30
grams. Leave your answer in 4 decimal places.
Transcribed Image Text:Question 5 (a) "The central limit theorem states that if X1, X2, ... X, are independent and identically distributed random variables, each having mean u and variance o?, then the distribution of X; tends to a normal distribution with mean u and variance o?." The statement above is erroneous. Point out the incorrect parts and explain why they are incorrect. (b) It is known that the mean weight u of packages of a certain brand of supplement pills is 5.02 grams. Find the probability that a random sample of 100 such packages will have a mean weight between 4.96 and 5.00 grams. Assume that the standard deviation o is 0.30 grams. Leave your answer in 4 decimal places.
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