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?\n1.5\n2.7\n3.0\n3.8

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?\n1.5\n2.7\n3.0\n3.8

Answer

Explanation:

Step1: Recall the property of standard - deviation

In a normal - like distribution, most data (about 68%) lies 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 for the range 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 $\mu = 7.5$. Substituting $\mu = 7.5$ into $\mu-\sigma=6$, we get $7.5-\sigma=6$. Solving for $\sigma$, we have $\sigma=7.5 - 6=1.5$. Also, if we use $\mu+\sigma = 9$ and $\mu = 7.5$, then $7.5+\sigma=9$, and $\sigma=9 - 7.5 = 1.5$.

Answer:

1.5