Question

**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.

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

Which of the following statements is not consistent with
the Central Limit Theorem?
1. The Central Limit Theorem applies to non-normal population
distributions.
2. The standard deviation of the sampling distribution will be
equal to the population standard deviation.
3. The sampling distribution will be approximately normal when
the sample size is sufficiently large.
4. The mean of the sampling distribution will be equal to the
population mean.

The Central Limit Theorem allows us to make predictions about
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One way it does this is by explaining (using a formula) how the
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The distribution of the population is exactly Normal.
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Why is the Central Limit Theorem considered to be so important
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The Central Limit Theorem says that when sample size n is taken
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a
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