Assuming a normal distribution of IQ scores with a mean of 100 and standard devi

Question

Assuming a normal distribution of IQ scores with a mean of 100 and standard deviation of 15, answer the following questions:
a.) What raw scores (x-values) make up the middle 50% of the distribution? Remember you need a range of scores here.
b.) What raw scores (x-values) make up the middle 75% of the distribution? Again, you need a range.
c.) What raw scores (x-values) make up the 8th percentile to the 65th percentile. You will also need a range for this one, but be careful as it will require a different strategy from a and b. Drawing will help.

Explanation / Answer

Answer to the question is as follows:

The params of normal distribution is Mean = 100, SD = 15

a. Middle 50 %' Z is .675

So, X values are : Mean +/- Z*SD = 100 +/- .675*15 = 89.875 to 110.125

b. Middle 75%' Z is 1.15
So, X values are Mean +/- Z*SD = 100 +/- 1.15*15 = 82.75 to 117.25

c. P( 8th to 65th percentile) = ?
Z value for 8th percentile is -2.41.
So, X value for 8th percentile is -2.41*15+100 = 63.85

So, X value for 65 percentile is .385.
So, X value for 65th percentile is .385*15+100 = 105.775

So, the limits of 8th and 65th percentile are 63.85 to 105.775

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