SOLUTION: The class average on a test is 85% with a standard deviation of 3%. Assuming that the marks are normally distributed, what mark range would 80% of the students fall within?

Question 1081612: The class average on a test is 85% with a standard deviation of 3%. Assuming that the marks are normally distributed, what mark range would 80% of the students fall within?
Answer by stanbon(75887) (Show Source): You can put this solution on YOUR website!
The class average on a test is 85% with a standard deviation of 3%. Assuming that the marks are normally distributed, what mark range would 80% of the students fall within?
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Sketch the picture.
You have a normal curve with p = 0.85 and s = 0.03
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Assuming you want the 80% to be centered on p = 0.85,
your have a left-tail of 10% and a right-tail of 10%.
left-tail z-value is invNorm(0.10) = -1.2816
right-tail z-value is invNorm(0.90) = +1.2816
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Find the corresponding mark values using x = z*s + p
Left-limit:: x = -1.2816*0.03+0.85
Right-limit:: x = +1.2816*0.03+0.85
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Cheers,
Stan H.
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