Question

In general, when we have a normal distribution, we change it to the standard normal distribution. What is the reason for that??

Answer 1

In general, when we have a normal distribution, we change it to the standard normal distribution because the transformation of a normal variable to a standard normal distribution does not affect the characteristics of the distribution. Hence, it helps and easier to compute required probabilities for different normal distributions. For example, the time taken by male and female athletes to complete a 400-meter race follows the normal distribution. The mean and standard deviation for males is 4 minutes and 1 minute whereas for females 5 minutes and 2 minute. If John completes the race at 3 minutes and Eva completes the race at 4 minutes. Among John and Eva, which one is the best within their gender. In this question, we can compute the probability by transforming to standard normal and can compare their performances.