Many states assess the skills of their students in various g

Many states assess the skills of their students in various grades. One program that is available for this purpose is the National Assessment of Educational Progress (NAEP). For eighth-grade students the average music score is approximately Normal with mean 142 and the standard deviation 35.

(a) Make a table that includes values (±0.01) of the scores corresponding to plus or minus one, two, and three standard deviations from the mean.

(b) Make a table that includes intervals (±0.01) of the scores, where approximately 68%, 95% and 99.7% of the average music scores fall.

Solution

As Mean (X) = 142

standard deviation (s) = 35

Then

a)

Standard deviations from the mean       Value
-3                       145 - 3(35) = 40
-2                       145 - 2(35) = 75
-1                       145 - 1(35) = 110
1                       145 + 1(35) = 180
2                       145 + 2(35) = 215
3                       145 + 3(35) = 250

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b)

From the table above, the intervals are

Description Interval

+/-1 standard deviation from the mean 110-180

+/-2 standard deviation from the mean 75-215

+/-3 standard deviation from the mean 40-250