Question

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.

Answer #1

Central limit theorem :

If the random variables X1,X2, .....Xn are a random sample of size n from any distribution with finite mean and variance , then the distribution of SAMPLE MEAN, will be approximately normal with standard deviation of

the statement in the given question , the term sample mean is missing

Distribution of sample mean follow Normal with mean =

and standard deviation ,

when n is large

Review: Central Limit Theorem
1 point possible (graded)
The Central Limit Theorem states that if
X1,…,Xn are i.i.d. and
E[X1]=μ<∞
;
Var(X1)=σ2<∞,
then
n−−√[(1n∑i=1nXi)−μ]−→−−n→∞(d)Wwhere W∼N(0,?).
What is Var(W)? (Express your answer in terms of n, μ and
σ).

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.

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...

Given a population with mean μ=100 and variance
σ2=81, the Central Limit Theorem applies
when the sample size n≥30. A random sample of size
n=30 is obtained.
What are the mean, the variance, and the standard deviation of
the sampling distribution for the sample mean?
Describe the probability distribution of the sample mean and
draw the graph of this probability distribution with its mean and
standard deviation.
What is the probability that x<101.5?
What is the probability that x>102?
What...

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.

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.

(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...

Hello, please review the statement below and determine if the
statement is right or not (and why).
Explain the central limit theorem
The central limit theorem states that when there’s a large
enough sample size (generally 30 or more) with a finite level of
variance, then the mean from all of the samples, from the same
population, will be approximately equal to the mean of the
population. There are three different components of the theorem.
The first is successive sampling...

Apply the Central Limit Theorem for Sample
Means
A population of values has a normal distribution with μ=77 and
σ=9.2. You intend to draw a random sample of size n=30.
Find the probability that a sample of size n=30n=30 is randomly
selected with a mean less than 76.8.
P(M < 76.8) =
Enter your answers as numbers accurate to 4 decimal places.
Answers obtained using exact z-scores or
z-scores rounded to 3 decimal places are accepted.

Which of the following is NOT a conclusion of the Central Limit
Theorem? Choose the correct answer below.
A. The distribution of the sample means x overbar will, as the
sample size increases, approach a normal distribution.
B. The mean of all sample means is the population mean mu.
C. The distribution of the sample data will approach a normal
distribution as the sample size increases.
D. The standard deviation of all sample means is the population
standard deviation divided...

ADVERTISEMENT

Get Answers For Free

Most questions answered within 1 hours.

ADVERTISEMENT

asked 1 minute ago

asked 2 minutes ago

asked 2 minutes ago

asked 3 minutes ago

asked 3 minutes ago

asked 3 minutes ago

asked 3 minutes ago

asked 4 minutes ago

asked 4 minutes ago

asked 4 minutes ago

asked 4 minutes ago

asked 5 minutes ago