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Question Central Limit Theorem a)According to the Central Limit Theorem, what are the mean and standard...

Question Central Limit Theorem

a)According to the Central Limit Theorem, what are the mean and standard deviation of the sampling distribution of sample means?

b)A population has a mean ?=1800 and a standard deviation ?=40. Find the mean and standard deviation of the sampling distribution of sample means when the sample size n=100.

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Answer #1

Solution :

(a)

According to the Central Limit Theorem, what are the mean and standard

deviation of the sampling distribution of sample means are,

= and

(b)

Given that,

mean = = 1800

standard deviation = = 40

n = 100

The sampling distribution of mean and standard deviation is ,

= 1800 and

= / n = 400 / 100 = 400 / 10 = 40

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