Question 1127845: Hello, guys. I desperately need all your help please. I have been trying to do these questions and it's incredibly struggling. Please help me!
For a normally disturbed population with a mean of U= 20 and a standard deviation of o = 5, a sample of N = 25 is drawn.
1. Find the probability of getting a average score greater than 21, (P x bar > 21)
2. Find the probability of getting a average score less than 19, (P x bar < 19)
3. Find the probability of getting a average score between 18 and 21, (P 18 < x bar < 21)
4. Find the average score that will separate out the bottom 80 % of scores.
Please help, I would really appericate it.
Answer by jim_thompson5910(35256)   (Show Source):
You can put this solution on YOUR website!
There are a lot of problems here. I'll go over problem 1 to help get you started. If you still have trouble with the others, then please let me know. Thank you.
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Problem 1
 is the greek letter sigma for the population standard deviation. In this case, 
n = 25 is the sample size
Use those two values to find the standard error.
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 is the greek letter mu for the population mean. It looks like a letter U but it's not. In this case, 
xbar or  is the sample mean. In the case of problem 1, it would be xbar = 21.
Use the xbar, mu and SE values to find the z score
Now use a table such as this one to find that  = 0.8413) ; in other words, the area to the left of z = 1 is about 0.8413
note: look on page 2 for the row that starts with 1.0, then look at the column that has 0.00 at the top. This row and column intersect with the value 0.8413 inside
So this means,
 = 1-P(Z < 1) = 1-0.8413 = 0.1587)
 = 0.1587)
This is approximate to four decimal places
Therefore,
 = 0.1587)
which is also approximate
If we use a calculator such as this one then we will find the answer is the same as found with the table
note: I typed in
Mean = 0
SD = 1
then I clicked the "above" radio button and typed "1" into the box.
After all that, I hit the "recalculate" button to produce the answer 0.1587
The image above shows the standard normal curve with the proper area shaded. That shaded area represents everything under the curve to the right of z = 1.
The final answer to problem 1 is approximately 0.1587
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