Question

How do you find the X value that corresponds to a given percentile of the normal distribution?Find the Z value corresponding to the given percentile, and then use the equation

Answer 1

When we have a normal distribution for a randome variable X we know its mean μ and its standard deviation σ.

We can normalize this function to the standard normal distribution (mean 0 and standard deviation 1) by calculating the z-score for any value of X.

This can be done as:

$z=\frac{X-\mu}{\sigma}$

Percentiles can be asociated to its corresponding z-score.

For example, percentil 30th correspond approximately to z = -0.5.

Then, using the previous equation, if we know z we can calculate its corresponding X as:

$X=\mu+z\cdot\sigma$

This converts the standard normal distribution back into the distribution that corresponds to X.

Answer: X = μ + zσ [First option]