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: Recall the formula for data within 1 standard deviation

The range within 1 standard deviation of the mean \(\mu\) is \(\mu - \sigma\) to \(\mu + \sigma\), where \(\sigma\) is the standard deviation.
We know \(\mu = 7.5\), \(\mu - \sigma = 6\) and \(\mu + \sigma = 9\) (or we can use one of the equations, say \(\mu - \sigma = 6\)).

Step2: Solve for \(\sigma\)

Substitute \(\mu = 7.5\) into \(\mu - \sigma = 6\):
\(7.5 - \sigma = 6\)
Subtract 7.5 from both sides:
\(-\sigma = 6 - 7.5\)
\(-\sigma = -1.5\)
Multiply both sides by -1:
\(\sigma = 1.5\)

Answer:

1.5