Question

Why is the standard normal curve so useful? Why do we use the standard normal curve to find percentiles instead of the normal curve of the original data?

Answer 1

Standard normal curve is useful because by standardization we can convert the raw measurements into Z scores. These Z scores can be in turn used to calculate percentiles. By standardizing we can apply central limit theorem for a large number of values.

A normal distribution can be used to find the area under the curve which actually represents the percentile value. To do so we standardize the normal distribution and caluculate the corresponding Z scores to find the value of area under the curve from a standard normal table. For this process a standard normal curve is always used because there are an infinite number of different normal distribution for which a table cannot be printed. Hence we have to always use the standard normal curve to find percentiles instead of the normal curve of the original data.