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

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

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

Answer

Answer:

A. 1.5

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 $a = 6$ to $b = 9$.

Step2: Use the formula for range within 1 standard deviation

The formula for the range of values within 1 standard deviation of the mean is $\mu-\sigma$ and $\mu + \sigma$. Let the standard deviation be $\sigma$. We know that $\mu-\sigma=6$ and $\mu+\sigma = 9$ with $\mu = 7.5$. Substituting $\mu = 7.5$ into $\mu-\sigma=6$ gives $7.5-\sigma=6$, so $\sigma=7.5 - 6=1.5$. Also, substituting into $\mu+\sigma = 9$ gives $7.5+\sigma=9$, so $\sigma=9 - 7.5 = 1.5$.