A population with normal distribution, with mean $167$ and standard deviation $3$ Assume that stature of men in a population with normal distribution has mean $167$cm and standard deviation $3$cm. Assume that $100$ men are chosen from this population independently. Question : 1. Find the probability that at least $55$ person's stature is less than $167$cm. 2. Find the probability that the mean of their statures is more than $167.6$cm. Note : My problem is that i don't know how to relate standard deviation and mean, to the probabilities that question wants. Actually, this is a question that one of my relatives asked me and i didn't know how to solve... So i put it here.

Let $H$ denote the height of a person. Then you want $$\mathbb{P}(H<167)=\mathbb{P}(Z<\frac{167-167}{3})=1/2$$ Where $Z$ is a standard normal random variable. Now you can use $\mu = np$ and $\sigma ^2=np(1-p)$, where $p=1/2$ to figure out the mean and standard deviation of your sample for use in a normal approximation to the binomial distribution.
This can be done as follows $$\mu = 100(\frac 12)=50 \quad \sigma = \sqrt{100(\frac 12)(1-\frac 12)}=5$$ Then you need (letting $N$ denote the number of people taller than $167$) $\mathbb{P}(N \ge 55)\approx \mathbb{P}(N > 55-0.5)=1-\mathbb{P}(Z < \frac{55-0.5-50}{5})=1-\mathbb{P}(Z<0.9)\approx 0.18$
For the other question it should be the same procedure with different numbers.