Question

Question Central Limit Theorem a)According to the Central Limit Theorem, what are the mean and standard...

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.

Math   Statistics-And-Probability   
0 0
Add a commentTranscribed image text
Next >

Homework Answers

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

0 0
Know the answer?
Your Answer:

Post as a guest

Your Name:

What's your source?

Earn Coins

Coins can be redeemed for fabulous gifts.

Log In

Sign Up

Not the answer you're looking for?
Ask your own homework help question
Similar Questions
Which of the following statements is not consistent with the Central Limit Theorem? 1. The Central...
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 where a sample mean will fall...
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...
Given a population with mean μ=100 and variance σ2=81, the Central Limit Theorem applies when the...
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...
What is wrong with the following statement of the central limit theorem? Central Limit Theorem.  If the...
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.
According to the central limit theorem, if a sample of size 81 is drawn from a...
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
According to the central limit theorem, a sample mean distribution is aproximately a normal distribution ,...
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 ?
Which of the following is NOT a conclusion of the Central Limit​ Theorem? Choose the correct...
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...
The Central Limit Theorem says that when sample size n is taken from any population with...
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.
Why is the Central Limit Theorem considered to be so important for inferential statistics? Consider the...
Why is the Central Limit Theorem considered to be so important for inferential statistics? Consider the mean, standard error, and shape of the sampling distribution of the means in your answer. Also describe the role played, if any, by the underlying or population distribution, sample distribution, and sampling distribution.
(05.02 LC) The Central Limit Theorem says that when sample size n is taken from any...
(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...
ADVERTISEMENT
Need Online Homework Help?

Get Answers For Free
Most questions answered within 1 hours.

Ask a Question
ADVERTISEMENT