If SAT math scores are bell-shaped with mean 400 and range from 0 to 800, estimate the standard deviation.
To estimate the standard deviation of the SAT math scores, we can use the range rule of thumb. According to this rule, we can estimate the standard deviation by taking one-fourth of the range and dividing it by a constant factor known as Z-factor.
In this case, the range of the SAT math scores is from 0 to 800, so the range is 800 - 0 = 800. Taking one-fourth of the range gives us 800/4 = 200.
The Z-factor is a constant factor that we use based on the shape of the bell curve. For a symmetrical bell-shaped curve, such as the SAT math scores in this case, the Z-factor is approximately 1.25.
To estimate the standard deviation, we divide the one-fourth of the range by the Z-factor:
Standard deviation ≈ (Range/4) / Z-factor = 200 / 1.25 = 160
Therefore, we can estimate that the standard deviation of SAT math scores is approximately 160.