SOLUTION: Assume a normal distribution with a mean of 80 and a standard deviation of 3. What limits would include the middle 55% of the cases

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Question 1000723: Assume a normal distribution with a mean of 80 and a standard deviation of 3. What limits would include the middle 55% of the cases
Found 2 solutions by stanbon, Boreal:
Answer by stanbon(75887) About Me  (Show Source):
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Assume a normal distribution with a mean of 80 and a standard deviation of 3. What limits would include the middle 55% of the cases
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Draw the picture.
You have a normal curve with 80 in the middle and 55% of the area around the mean.
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The left tail is 0.5-0.55/2 = 0.225
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Find the z-value with that tail::
invNorm(0.225) = -0.7554
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Find the corresponding x value::
x = -0.7554*3 + 80 = 77.734-------lower limit
x = +0.7554*3 + 80 = 82.266-------upper limit
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Cheers,
Stan H.
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Answer by Boreal(15235) About Me  (Show Source):
You can put this solution on YOUR website!
Find the z-value for 0.2250 probability. It will be negative. Find the z-value for the 0.7750 probability. They will be the same with opposite signs.
That is -0.755 (rounding).
The z-value for 0.7750 is 0.755
This is +/- 0.755 SD or +/- 2.265
The limits are (77.735, 82.265)
It helps a lot to draw the distribution when doing these problems.