Question

The Central Limit Theorem says that when sample size n is taken from any population with mean μ and standard deviation σ when n is large, which of the following statements are true?

- The distribution of the sample mean is approximately Normal.
- The standard deviation is equal to that of the population.
- The distribution of the population is exactly Normal.
- The distribution is biased.

Answer #1

**Solution:**

Given: The Central Limit Theorem says that when sample size n is
taken from any population with mean μ and standard deviation σ when
n is large, then **the distribution of the sample mean is
approximately Normal.**

**thus first options is correct.**

In this case standard deviation of sample means = which is not equal to population standard deviation, thus second option is not correct.

Since population distribution is unknown, we can not say distribution is exactly Normal. Thus third option is not correct.

We either say distribution is normally or approximately Normal or Non-normal, so fourth option is not correct.

(05.02 LC)
The Central Limit Theorem says that when sample size n is taken
from any population with mean μ and standard deviation σ when n is
large, which of the following statements are true? (4 points)
I. The distribution of the sample mean is exactly Normal.
II. The distribution of the sample mean is approximately
Normal.
III. The standard deviation is equal to that of the
population.
IV. The distribution of the population is exactly Normal.
a
I and...

What is wrong with the following statement of the central limit
theorem?
Central Limit Theorem. If the random variables X1,
X2, X3, …, Xn are a random sample of size n from any distribution
with finite mean μ and variance σ2, then the distribution of will
be approximately normal, with a standard deviation of σ / √n.

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.

Which one of the following statements is
true?
A. The Central Limit Theorem states that the sampling
distribution of the sample mean, y , is approximately
Normal for large n only if the distribution of the population is
normal.
B. The Central Limit Theorem states that the sampling
distribution of the sample mean, y , is approximately
Normal for small n only if the distribution of the population is
normal.
C. The Central Limit Theorem states that the sampling
distribution...

a) What is the Central Limit Theorem? It is always true
that as the sample size, n, increases, the distribution of the
sample means will be approximately normally distributed.
Explain
b) If the underlying population of study is not normally
distributed, how large should the sample size be? What if the
population is normally distributed ?

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.

The Central Limit Theorem is used when dealing with: mean from a
sample, individual data point ,chi-squared distributions, or
sampling distribution of a standard deviation? When using the CLT,
we use σ √ n for the: standard deviation for individual values,
mean for the sample, standard deviation of the sample means, or
sample size?

Apply the Central Limit Theorem for Sample Means A population of
values has a normal distribution with μ = 220 and σ = 33.8. You
intend to draw a random sample of size n = 35.
Find the probability that a single randomly selected value from
the population is less than 224.

5.26 What is wrong? Explain what is wrong in each of the
following statements.
(a) The central limit theorem states that for large n,
the population mean μ is approximately Normal.
(b) For large n, the distribution of observed values
will be approximately Normal.
(c) For sufficiently large n, the 68–95–99.7 rule says
that x¯x¯ should be within μ ± 2σ about 95% of
the time.
(d) As long as the sample size n is less than half the
population...

According to the central limit theorem, if a sample of size 81
is drawn from a population with a variance of 16, the standard
deviation of the distribution of the sample means would equal
_______.
.98
.44
.68
.87
.75

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