Question

According to the central limit theorem, a sample mean distribution
is aproximately a normal distribution , what are the mean and
standard deviation of this normal distribution ?

Answer #1

Solution :

Given that ,

According to the central limit theorem,

mean =

standard deviation =

n = sample size

sample distribution of sample mean is ,

=

sampling distribution of standard deviation

= / n

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.

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.

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

The Central Limit Theorem allows us to make predictions about
where a sample mean will fall in a distribution of sample means.
One way it does this is by explaining (using a formula) how the
shape of the distribution will change depending on the sample size.
What part of the Central Limit Theorem tells us about the shape of
the distribution?
The part that explains that there is no standardized table you
can use to find probabilities once you use...

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.

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...

Based on the Central Limit Theorem, in which of the following
situations will the sampling distribution of the sample mean NOT be
normally distributed?
If we sample 14 grocery receipts from a distribution of all
receipts with a mean of $128 and a standard deviation of$23.
If we sample 50 recent home sales from a distribution of all
home sales in the local area with a mean sales price of$315,200 and
a standard deviation of $4,700.
If we sample 10...

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.

The Central Limit Theorem indicates that in selecting random
samples from a population, the sampling distribution of the the
sample mean x-bar can be approximated by a normal distribution as
the sample size becomes large.
Select one: True False

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