Statistics - Sampling Methods and Central Limit Theorem

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"Information from the American Institute of Insurance indicates the mean amount of life insurance per household in the United States is $110,000. This distribution follows the normal distribution with a standard deviation of $40,000.
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What is the sampling distribution of sample means?
What is the mean of the sampling distribution of sample means?
What is its standard deviation?
How is that standard deviation affected by the sample size?
What does the centrallimittheorem state about that distribution?

Why is the CentralLimitTheorem so important to the study of sampling distributions?
A. It allows us to disregard the size of the sample selected when the population is not normal
B. It allows us to disregard the shape of the sampling distributions when the size of the population is large
C. It allows us to disregard

Sampling Distribution and the CentralLimitTheorem
Find the probabilities.
a. From National Weather Service records, the annual snowfall in the TopKick Mountains has a mean of 92 inches and a standard deviation ? of 12 inches. If the snowfall from 25 randomly selected years are chosen, what it the probability that the

What is the CentralLimitTheorem? How large should the sample size be if the underlying distribution of the population values are:
a. Normally distributed (discuss).
b. Non-normally distributed. (discuss)
2. What is the difference, if any, between the standard deviation of the sample and the standard error of the mean

#1
Answer the following based upon the implications of the CentralLimitTheorem (assume sample size larger than 30 when samples are mentioned in (a) and (b) below).
a) How does the mean of the sampling distribution of all possible sample means from a population compare to the mean of the population?
b) How does the stan

See attached file for proper formatting.
4. The amount of time a doctor spends in an appointment with a new patient has a
mean minutes and standard deviation minutes. The distribution of
times is not normal.
(a) Suppose a sample of 5 new patient appointments is
selected. What can you say about the sampling dis

If a particular batch of data is approximately normally distributed, we would find that approximately:
a. 2 of every 3 observations would fall between ±1 standard deviation around the mean.
b. 4 of every 5 observations would fall between ±1.28 standard deviations around the mean.
c. 19 of every 20 observations would fall be

See the attached file.
If X1,X2,..., Xn, are (iid) , from a distribution with mean μ and variance σ^2. Define the sample mean as
Xbar = (X1+X2+...+Xn) / n
(a) Show that the mean and variances of the probability density function of Xbar are given as E(Xbar) = μ
Var(Xbar) = (σ^2)/n
b