Originally Posted by

**lllll** A soil scientist wants estimate the average pH for a large field by randomly selecting 40 core samples. Although the population standard deviation of pH is not know, past experiences indicates that most soils have a pH value between 5 and 8. Find the approximate probability that the sample mean will be within .2 units of the true average pH.

$\displaystyle P\left( -\frac{0.2}{\sigma/\sqrt{40}} \leq \frac{\overline{Y}-\mu}{\sigma/\sqrt{n}} \leq \frac{0.2}{\sigma/\sqrt{40}}\right)$

$\displaystyle P\left( -\frac{0.2}{\sigma/\sqrt{40}} \leq Z \leq \frac{0.2}{\sigma/\sqrt{40}}\right)$

I'm just have trouble deciding on a $\displaystyle \sigma$, since it's between 5 and 8, I'm not sure if I should just take an average which is 6.5, or if there's some other way of getting it.