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 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...

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...

Given a population with a mean of μ=105 and a variance of
σ2=36, the central limit theorem applies when the sample size is
n≥25. A random sample of size n=25 is obtained.
a. What are the mean and variance of the sampling distribution
for the sample means?
b. What is the probability that x>107?
c. What is the probability that 104<x<106?
d. What is the probability that x≤105.5?

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.

ADVERTISEMENT

Get Answers For Free

Most questions answered within 1 hours.

ADVERTISEMENT

asked 22 minutes ago

asked 22 minutes ago

asked 32 minutes ago

asked 55 minutes ago

asked 1 hour ago

asked 1 hour ago

asked 1 hour ago

asked 2 hours ago

asked 2 hours ago

asked 2 hours ago

asked 3 hours ago

asked 3 hours ago