the mean shoe size of the students in a math class is 7.5. most of the shoe sizes fall within 1 standard…

Explanation:

Step1: Recall standard - deviation property

In a normal - like distribution, most data (about 68%) falls within 1 standard deviation of the mean. If the mean is $\mu = 7.5$ and the range within 1 standard deviation is from 6 to 9.

Step2: Calculate the standard deviation

The formula to find the lower and upper bounds within 1 standard deviation of the mean is $\mu-\sigma$ and $\mu + \sigma$ respectively. Let the standard deviation be $\sigma$. We know that $\mu-\sigma=6$ and $\mu = 7.5$. Substituting $\mu = 7.5$ into $\mu-\sigma=6$, we get $7.5-\sigma=6$. Solving for $\sigma$: [ \begin{align*} 7.5-\sigma&=6\ -\sigma&=6 - 7.5\ -\sigma&=- 1.5\ \sigma&=1.5 \end{align*} ] We can also use the upper - bound formula $\mu+\sigma = 9$. Substituting $\mu = 7.5$ into $\mu+\sigma=9$, we have $7.5+\sigma=9$, then $\sigma=9 - 7.5=1.5$.

Answer:

1.5