SOLUTION: Consider a normal population with a mean of 25 and standard deviation of 8.0. A)Calculate the standard score for a value x of 27. B)Calculate the standard score for a randoml

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Question 424494: Consider a normal population with a mean of 25 and standard deviation of 8.0.
A)Calculate the standard score for a value x of 27.
B)Calculate the standard score for a randomly selected sample of 45 with x = 27.
Explain why the standard scores of 27 are different between A and B above
Do I use the formula z=x-mu/(std dev/sqrt(n))
z=27-25/(8.0/sqrt(n))
I would appreciate any guidance with the above problem.
Thank You
Becky

Answer by stanbon(75887) (Show Source):
You can put this solution on YOUR website!
Consider a normal population with a mean of 25 and standard deviation of 8.0.
A)Calculate the standard score for a value x of 27.
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z(27)=(27-25)/8 = 2/8 = 1/4
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B)Calculate the standard score for a randomly
selected sample of 45 with x = 27.
z(27) = (27-25)/[8/sqrt(45)] = 1.6771
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Explain why the standard scores of 27 are different between A and B above
The std for the population is 8
The std for the sample means is 8/sqrt(45)
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Cheers,
Stan H.
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