Question

The population has mean μ=29 and standard deviation σ=9.

This distribution is shown with the black dotted line.

We are asked for the mean and standard deviation of the
sampling distribution for a sample of size 34. The Central Limit
Theorem states that the sample mean of a sample of size n is
normally distributed with mean μx¯=μ and σx¯=σn√.

In our case, we have μ=29, σ=9, and n=34. So,

μx¯=29

and

σx¯=934‾‾‾√=1.5

This distribution is shown with the red solid line. Notice the
sampling distribution, which represents the sample mean of random
values of the population, has the same mean as the population
distribution. However, the sample mean will vary less than a random
value from the population, and therefore has a smaller standard
deviation.

Content attribution- Opens a dialog

Use the Central Limit Theorem for Means to find the sample
mean and the sample standard deviation

Question

What is the probability that the sample mean for a sample of
size 34 will be more than 32?

Use the results from above in your calculation and round your
answer to the nearest percent. You may use a calculator or the
portion of the z-table given below.

z0.40.50.60.70.80.91.01.11.21.31.41.51.61.71.81.92.02.12.22.32.42.52.60.000.65540.69150.72570.75800.78810.81590.84130.86430.88490.90320.91920.93320.94520.95540.96410.97130.97720.98210.98610.98930.99180.99380.99530.010.65910.69500.72910.76110.79100.81860.84380.86650.88690.90490.92070.93450.94630.95640.96490.97190.97780.98260.98640.98960.99200.99400.99550.020.66280.69850.73240.76420.79390.82120.84610.86860.88880.90660.92220.93570.94740.95730.96560.97260.97830.98300.98680.98980.99220.99410.99560.030.66640.70190.73570.76730.79670.82380.84850.87080.89070.90820.92360.93700.94840.95820.96640.97320.97880.98340.98710.99010.99250.99430.99570.040.67000.70540.73890.77040.79950.82640.85080.87290.89250.90990.92510.93820.94950.95910.96710.97380.97930.98380.98750.99040.99270.99450.99590.050.67360.70880.74220.77340.80230.82890.85310.87490.89440.91150.92650.93940.95050.95990.96780.97440.97980.98420.98780.99060.99290.99460.99600.060.67720.71230.74540.77640.80510.83150.85540.87700.89620.91310.92790.94060.95150.96080.96860.97500.98030.98460.98810.99090.99310.99480.99610.070.68080.71570.74860.77940.80780.83400.85770.87900.89800.91470.92920.94180.95250.96160.96930.97560.98080.98500.98840.99110.99320.99490.99620.080.68440.71900.75170.78230.81060.83650.85990.88100.89970.91620.93060.94290.95350.96250.96990.97610.98120.98540.98870.99130.99340.99510.99630.090

Answer #1

A population has a mean μ=78 and a standard deviation σ=22. Find
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μx= ?????

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(Round σx to two decimal places.)
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(Round σx to two decimal places.)
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(Round σx to two decimal places.) μx = σx = Describe the
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Describe the distribution of x values for sample size n = 16.
(Round σx to two decimal places.) μx = σx = Describe the
distribution of x values for sample size n = 100. (Round σx to two
decimal places.) μx...

Suppose x has a normal distribution with mean
μ = 57 and standard deviation σ = 7.
Describe the distribution of x values for sample size
n = 4. (Round σx to two
decimal places.)
μx
σx
Describe the distribution of x values for sample size
n = 16. (Round σx to two
decimal places.)
μx
σx
Describe the distribution of x values for sample size
n = 100. (Round σx to two
decimal places.)
μx
σx
How do the...

Given a population with a mean of µ = 230 and a standard
deviation σ = 35, assume the central limit theorem applies when the
sample size is n ≥ 25. A random sample of size n = 185 is obtained.
Calculate σx⎯⎯

Suppose x has a normal distribution with mean
μ = 31 and standard deviation σ = 11.
Describe the distribution of x values for sample size
n = 4. (Round σx to two
decimal places.)
μx
=
σx
=
Describe the distribution of x values for sample size
n = 16. (Round σx to two
decimal places.)
μx
=
σx
=
Describe the distribution of x values for sample size
n = 100. (Round σx to two
decimal places.)
μx...

Suppose x has a distribution with μ = 29 and
σ = 24.
(a)
If a random sample of size n = 31 is drawn, find
μx, σx
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σx to two decimal places and the
probability to three decimal places.)
μx=σx=P(29
≤ x ≤ 31)=
(b)
If a random sample of size n = 72 is drawn, find
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and P(29 ≤ x ≤ 31). (Round
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Suppose x has a distribution with μ = 29 and σ = 25.
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μx =
σ x =
P(29 ≤ x ≤ 31) =
(b) If a random sample of size n = 71 is drawn, find μx, σ x
and P(29 ≤ x ≤...

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