attending to precision give the percent of the area under the normal curve represented by the shaded region…

Explanation:

Step1: Recall normal - curve properties

The total area under the normal curve is 1 or 100%. The area between $\mu - 3\sigma$ and $\mu - \sigma$ can be found using the empirical rule (68 - 95 - 99.7 rule) and the symmetry of the normal distribution. The area between $\mu - 3\sigma$ and $\mu+3\sigma$ is approximately 99.7%, the area between $\mu - 2\sigma$ and $\mu+2\sigma$ is approximately 95%, and the area between $\mu - \sigma$ and $\mu+\sigma$ is approximately 68%.

Step2: Calculate area between $\mu - 3\sigma$ and $\mu - \sigma$

The area between $\mu - 3\sigma$ and $\mu$ is half of the area between $\mu - 3\sigma$ and $\mu+3\sigma$, which is $\frac{99.7%}{2}=49.85%$. The area between $\mu - \sigma$ and $\mu$ is half of the area between $\mu - \sigma$ and $\mu+\sigma$, which is $\frac{68%}{2}=34%$. The area between $\mu - 3\sigma$ and $\mu - \sigma$ is $49.85% - 34%=15.85%$.

Answer:

15.85