Assume womens heights are normally distributed with a mean of 63.4inches and a standard deviation of 2.3inches. if 1 woman is randomly selected what is the probability that her height is less than 64in?

Question

kirbykirby · Answer

If $X$ is women's height in inches, then the problem is asking for $P(X<64)$. Since $X$ is normally distributed, you can standardize it and then you a standard normal table to find the probability:

$$P(X<64)= P\left( \frac{X-63.4}{2.3}<\frac{64-63.4}{2.3}\right)=P(Z<0.26)$$