**Re: What is the probability that the sample mean will be within 1 hour of the populat**

if you have an underlying population distribution with mean $\mu$ and standard deviation $\sigma$

and you take $N$ samples of that distribution and compute the mean of the sample, $\bar{X}$

then, provided $N$ is large enough $\bar{X}$ has an approximately normal distribution with mean $\mu$ and standard deviation $\dfrac{\sigma}{\sqrt{N}}$

In the given problem $N$ is large enough for this to be true.

given this you should be able to answer the questions.