SOLUTION: Suppose that the percentage returns for a given year for all stocks listed on the New York Stock Exchange are approximately normally distributed with a mean of 12.4 percent and

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Question 317453: Suppose that the percentage returns for a given year for all stocks listed on the New York Stock Exchange are approximately normally distributed with a mean of 12.4 percent and a standard deviation of 20.6 percent. Considering drawing a sample of n = 5 stocks. Find the mean and the standard deviation of the sampling distribution of X, and find an interval containing 95.44 percent of all possible sample mean returns.
I don't have any work to show because I have no idea where to start. I would appreciate any assistance you can give me. Thanking you in advance for your time and effort. Have a beautiful day.
Natasha j
Found 2 solutions by stanbon, butterflyinschool:
Answer by stanbon(75887) About Me  (Show Source):
You can put this solution on YOUR website!
Suppose that the percentage returns for a given year for all stocks listed on the New York Stock Exchange are approximately normally distributed with a mean of 12.4 percent and a standard deviation of 20.6 percent.
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Considering drawing a sample of n = 5 stocks. Find the mean and the standard deviation of the sampling distribution of X,
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The mean of the sample means of size n=5 = 12.4%
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The standard deviation of the sample means of size 5 = 20.6%/sqrt(5) = 0.0921
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Note: To understand this read what your text says about "The Central
Limit Theorem".
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Find an interval containing 95.44 percent of all possible sample mean returns.
---
Draw the picture of 95.44% centered on the mean. That puts 0.4772 to the
left of the middle, leaving a left-most tail of 0.0228.
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Find the z-value with a left tail of 0.0228
InvNorm(0.0228) = z = -1.999
Correspondingly, there is an upper bound of z = +1.999
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Find the corresponding x-values
x = zs + u
x = -1.999*0.0921 + 0.124 = -1.78%
x = 1.999*0.0921 + 0.124 = 30.81%
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Cheers,
Stan H.

Answer by butterflyinschool(1) About Me  (Show Source):
You can put this solution on YOUR website!
Suppose that the percentage returns for a given year for all stocks listed on the New York Stock Exchange are approximately normally distributed with a mean of 12.4 percent and a standard deviation of 20.6 percent.
-----------------
Considering drawing a sample of n = 5 stocks. Find the mean and the standard deviation of the sampling distribution of X,
---
The mean of the sample means of size n=5 = 12.4%
---
The standard deviation of the sample means of size 5 = 20.6%/sqrt(5) = 0.0921
-------------------
Note: To understand this read what your text says about "The Central
Limit Theorem".
-------------------
Find an interval containing 95.44 percent of all possible sample mean returns.
---
Draw the picture of 95.44% centered on the mean. That puts 0.4772 to the
left of the middle, leaving a left-most tail of 0.0228.
-------------
Find the z-value with a left tail of 0.0228
InvNorm(0.0228) = z = -1.999
Correspondingly, there is an upper bound of z = +1.999
--------------------------------
Find the corresponding x-values
x = zs + u
x = -1.999*0.0921 + 0.124 = -1.78%
x = 1.999*0.0921 + 0.124 = 30.81%