Question

the mean shoe size of the students in a math class is 7.5. most of the shoe sizes fall within 1 standard deviation, or between a size 6 and a size 9. what is the standard deviation of the shoe size data for the math class? 1.5 2.7 3.0 3.8

Explanation:

Step1: Use the formula for range within 1 standard deviation

If the mean is \(\mu = 7.5\) and the range within 1 standard deviation (\(\sigma\)) is from \(a = 6\) to \(b=9\). We know that for a normal - like distribution (where most data lies within 1 standard deviation of the mean), the formula for the range within 1 standard deviation is \(\mu-\sigma=a\) and \(\mu + \sigma=b\). We can also use \(b - a=( \mu+\sigma)-(\mu - \sigma)\).

Step2: Simplify the equation

Simplify \(b - a=( \mu+\sigma)-(\mu - \sigma)\).

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Substitute \(a = 6\) and \(b = 9\) into the equation \(b - a=2\sigma\). So \(9 - 6=2\sigma\).

Step3: Solve for \(\sigma\)

We have \(3 = 2\sigma\). Then \(\sigma=\frac{9 - 6}{2}\).

$$ \sigma=\frac{3}{2}=1.5 $$

Answer:

1.5