Question

A random sample of n = 100 observations is drawn from a population with mean equal to 21 and standard deviation equal to 20, i.e. population mean is 21 and population standard deviation is 20. Complete parts a through d below.

a. What is the probability distribution of ?̅? i.e., Give the mean and standard deviation of the sampling distribution of ?̅ and state whether it is normally distributed or not.

b. Find P ( 18.7 < ?̅ < 23.3 )

c. If standard deviation of population distribution is decreased to 10, would answer in b decrease or increase or not change? Why? (Hint: you don’t necessarily calculate the probability of P ( 18.7 < ?̅ < 23.3 ) to find the answer. Think about how the sampling distribution of ?̅ would change.)

d. If sample size increases to 200, would answer in b decrease or increase or not change? Why? (Hint: you don’t necessarily calculate the probability of P ( 18.7 < ?̅ < 23.3 ) to find the answer. Think about how the sampling distribution of ?̅ would change.)

Answer #1

Mean od the sampling distribution is 21

Standard deviation of the sampling distribution is

c. If standard deviation decreases then the probability will increase

d. If we increase the sample size to 200 then standard deviation of the sampling distribution will decrease and hence the probability increases

A random sample of n = 100 observations is drawn from a
population with mean equal to 21 and standard deviation equal to
20, i.e. population mean is 21 and population standard deviation is
20. Complete parts a through d below.
a. What is the probability distribution of ?̅? i.e., Give the
mean and standard deviation of the sampling distribution of ?̅ and
state whether it is normally distributed or not.
b. Find P ( 18.7 < ?̅ < 23.3...

A random sample of n=36 observations is drawn from a population
with a mean equal to 60 and a standard deviation equal to 36.
a. Find the probability that x? is less than 48 ____
b. Find the probability that x? is greater than 63____
c. Find the probability that x? falls between 48 and 78 ____

A random sample of n = 81 observations is drawn from a
population with a mean equal to 15 and a standard deviation equal
to 9 . Complete parts a through g below. a. Give the mean and
standard deviation of the? (repeated) sampling distribution x
overbar . mu Subscript x overbar equalsnothingsigma Subscript x
overbar equalsnothing ?(Type integers or? decimals.) b. Describe
the shape of the sampling distribution of x overbar . Does this
answer depend on the sample?...

A random sample of n=81 observations is drawn from a population
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Suppose a random sample of n = 25 observations is
selected from a population that is normally distributed with mean
equal to 108 and standard deviation equal to 14.
(a) Give the mean and the standard deviation of the sampling
distribution of the sample mean
x.
mean
standard deviation
(b) Find the probability that
x
exceeds 113. (Round your answer to four decimal places.)
(c) Find the probability that the sample mean deviates from the
population mean ? = 108...

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and standard deviation equal to 10.
a) Give the mean and the standard deviation of the sampling
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mean =
standard deviation =
b) Find the probability that x exceeds 106. (Round your
answer to four decimal places.)
c) Find the probability that the sample mean deviates from the
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Suppose that we will randomly select a sample of 79 measurements
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Normally distributed ; yes , because the sample size is large . (b)
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deviation to four decimal places.)
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standard deviation =
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and standard deviation σ = 10.
Determine the mean and standard deviation of the x sampling
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(a) n = 8 μ = σ =
(b) n = 14 μ = σ =
(c) n = 34 μ = σ =
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a. Describe the sampling distribution of the sample mean x bar.
(Hint: describe the shape, calculate the mean and the standard
deviation of the sampling distribution of x bar.
b. What is the probability that the sample mean is greater than
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