# Restricting the Normal Distribution to Positive Numbers

I'm working with a software library that generates random values from the standard normal distribution (mean=0, standard deviation=1).

Suppose the random values represent heights which have a mean=175 and standard deviation=10. They must be positive.

I convert from standard normal to normal using the formula Z=(X-mu)/sigma i.e. X=(Z*sigma)+mu e.g. 173.75=(-0.125*10)+175. In theory it's possible to get a value so small that it would imply a negative height e.g. -25=(-20*10)+175. What's the best way of handling this scenario? Which of the following is most appropriate?

1. Do nothing - it's so unlikely that it's not worth worrying about
2. Check for negative values and disregard them, regenerate a new random height
3. Define an absolute within the Normal Distribution model itself (I don't know if this is theoretically possible).

If $$X \sim N(175, 10^2)$$, then $$P(X \le 0) = \Phi(-175/10) \le 7.2 \times 10^{-69}$$. It is extremely unlikely to get a negative height, but still possible.