the heights of the students at a particular high school are normally distributed. 68% of the heights are…

Explanation:

Step1: Recall the empirical rule

For a normal - distribution, approximately 68% of the data lies within 1 standard deviation of the mean. That is, if the mean is $\mu$ and the standard deviation is $\sigma$, then $P(\mu-\sigma<X<\mu + \sigma)\approx0.68$.

Step2: Find the mean

The mean is the mid - point of the interval within which 68% of the data lies. The formula for the mean $\mu=\frac{57 + 71}{2}$. $\mu=\frac{128}{2}=64$

Step3: Find the standard deviation

Since the interval is from $\mu-\sigma$ to $\mu+\sigma$, and the lower bound is 57 and the mean $\mu = 64$, we can find $\sigma$ using $\mu-\sigma=57$. Substituting $\mu = 64$ into $\mu-\sigma=57$, we get $64-\sigma=57$, so $\sigma=64 - 57=7$.

Answer:

mean: 64 standard deviation: 7