Question

A random sample of size n=16 is take from a normal population
with μ=40 and σ^{2}=32. Find the probability that the
sample mean is greater than or equal to 38.

Answer #1

= P(Z > -1.41)

= 1 - P(Z < -1.41)

= 1 - 0.0793

= 0.9207

A random sample of size n = 241 is taken from a
population of size N = 5,588 with mean μ = −68
and variance σ2 = 183. [You may find it
useful to reference the z table.]
a-1. Is it necessary to apply the finite
population correction factor?
Yes
No
a-2. Calculate the expected value and the standard
error of the sample mean. (Negative values should be
indicated by a minus sign. Round "standard error" to 2
decimal places.)...

A random sample of n = 25 is selected from a normal population
with mean μ = 101 and standard deviation σ = 13.
(a) Find the probability that x exceeds 108. (Round your answer
to four decimal places.)
(b) Find the probability that the sample mean deviates from the
population mean μ = 101 by no more than 3. (Round your answer to
four decimal places.)

Suppose that we take a random sample of size n from a population
having a mean μ and a standard deviation of σ. What is the
probability or confidence we have that our sample will be within
+/- 1 of the population mean μ?
(a) μ = 10, σ = 2, n = 25

Suppose we take a random sample X1,…,X6 from a normal population
with an unknown variance σ2 and unknown mean μ.
Construct a two-sided 99% confidence interval for μ if the
observations are given by
2.59,0.89,2.69,0.04,−0.26,1.31

A random sample of n = 25 is selected from a normal
population with mean
μ = 102
and standard deviation
σ = 11.
(a)
Find the probability that
x
exceeds 107. (Round your answer to four decimal places.)
(b)
Find the probability that the sample mean deviates from the
population mean μ = 102 by no more than 2. (Round your
answer to four decimal places.)
You may need to use the appropriate appendix table or technology
to answer...

A simple random sample of size n=40 is obtained from a
population with μ = 50 a n d σ = 4. Does the population
distribution need to be normally distributed for the sampling
distribution of x ¯ to be approximately normally distributed? Why
or why not? What is the mean and standard deviation of the sampling
distribution?

Suppose a random sample of n = 16 observations is selected from
a population that is normally distributed with mean equal to 102
and standard deviation equal to 10.
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 106. (Round your
answer to four decimal places.)
c) Find the probability that the sample mean deviates from the
population mean μ...

Random samples of size n were selected from a
normal population with the means and variances
given here.
n = 25, μ = 12, σ2 = 9
Describe the shape of the sampling distribution of the sample
mean.
a. The distribution is normal
b. The distribution is skewed left
c. The distribution is bimodal
d. The distribution is uniform
e. The distribution is skewed right
Find the mean and the standard error of the sampling
distribution of the sample mean....

A random sample of size n = 186 is taken from a
population of size N = 5,613 with mean μ = −65
and variance σ2 = 183. [You may find it
useful to reference the z table.]
a-1. Is it necessary to apply the finite
population correction factor?
Yes
No
a-2. Calculate the expected value and the standard
error of the sample mean. (Negative values should be
indicated by a minus sign. Round "standard error" to 2
decimal places.)...

A random sample of size n1 = 25, taken from a normal
population with a standard deviation σ1 = 5.2, has a
sample mean = 85. A second random sample of size n2 =
36, taken from a different normal population with a standard
deviation σ2 = 3.4, has a sample mean = 83. Test the
claim that both means are equal at a 5% significance level. Find
P-value.

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