SOLUTION: I am having problems with normal distrubution problems and have no good example to follow. Could someone help me with the following problem and show steps of completetion. I grea

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Question 189871: I am having problems with normal distrubution problems and have no good example to follow. Could someone help me with the following problem and show steps of completetion. I greatly appreciate the help. Thanks in advance.
A normal distribution consists of 1000 scores with a mean of 100 and a standard deviation of 10. About how many of the scores are:
a. below 90
b. between 80 and 90
Answer by stanbon(75887) (Show Source):
You can put this solution on YOUR website!
A normal distribution consists of 1000 scores with a mean of 100 and a standard deviation of 10.
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About how many of the scores are:
a. below 90
z(90) = (90-100)/10 = -1 -------------that means 90 is one standard deviation
to the left of the mean.
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P(x < 90) = P(z< -1) = 0.50-0.341 = 0.159
How many scores are to the left of 90?:
0.159*1000 = 159 scores to the left of 90
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b. between 80 and 90
Draw the picture of the curve on the x-axis and another curve on the z-axis
z(80) = (80-100)/10 = -2
z(90) = -1
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P(80 < x < 90) = P(-2 < z < -1) = 0.1359
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Cheers,
Stan H.