When we convert normal distributions to the standard normal distribution, we are essentially making them all alike. How is this possible and what are the implications?

What will be an ideal response?

Normal distributions are bell-shaped and symmetric around their means. When a normal population is standardized, every value is replaced by a value equal to the number of standard deviations above or below the mean that particular value is. So in a normal population with mean 10 and standard deviation 2, the value 8 becomes z = -1 and so does the value 6 in a normal population with mean 10 and standard deviation 4. So, all normal populations become related to this one standard normal population. That is why, for every normal population 68.26% fall within ±1 standard deviation of the mean, 95.44% fall within 2 and 99.73% fall within ±3. The only thing that really matters for a normal distribution are the standardized z values. Once you know how many standard deviations above or below the mean a value in the normal population is, you can always determine that value and any probabilities about that value.