generate random number from normal distribution

Question

Can any one explain in which range I am going to get random numbers, if I was said generate random number from normal distribution with mean=50 and std_dev=25,

what does it exactly means..I tried to find the ans but have some doubts.

Answer 1

If there are N randomly generated numbers from normal distribution, and the mean, $\mu$, standard deviation, $\sigma$, the 68–95–99.7 rule, also known as the three-sigma rule or empirical rule, states that nearly all values lie within three standard deviations of the mean in a normal distribution.

68.27% of the values lie within one standard deviation of the mean. Similarly, 95.45% of the values lie within two standard deviations of the mean. Nearly all (99.73%) of the values lie within three standard deviations of the mean.

$ \begin{align} \Pr(\mu-\;\,\sigma \le x \le \mu+\;\,\sigma) &\approx 0.6827 \\ \Pr(\mu-2\sigma \le x \le \mu+2\sigma) &\approx 0.9545 \\ \Pr(\mu-3\sigma \le x \le \mu+3\sigma) &\approx 0.9973 \end{align} $

Answer 2

To solve this use Inverse Cumulative Distribution function. You need a uniform [0,1) random source (any would do), and you just sample InvCDF with those random numbers and it will produce the required result.