# Finding the probability that the temperature is between x and y

Hello I have a problem that I can't seem to come to the proper conclusion with. It is as follows:

What is the probability that a randomly selected day in August will have a temperature greater than 85 but less than 100. Mean is 80 with a std dev of 8 assuming temperature is distributed normally.

I missed this on a test and I'd like to know where I went wrong so if someone could work it out step by step I would appreciate it very much. Thanks

-
Are we assuming temperatures are normally distributed? –  Gerry Myerson Oct 31 '12 at 1:57
Yes my bad. Assume that the temperatures are normally distributed. –  Chris Maness Oct 31 '12 at 1:58

If your $\mu$ is 80, and $\sigma$ is 8, you're looking for $$P(85\le X \le 100)$$ Which can be found like this: $P(X\le 100)-P(X\le 85)$, letting $X=\frac{x-\mu}{\sigma}$ when you sub in your given info you can use the standard normal table and get your $z$ statistic (as I have been told they're called). So now you're looking to get $P(z \le 2.5)-P(z \le .625)$, and I'm assuming you can do the rest.