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

To find the x value that corresponds to a given percentile of the normal distribution, calculate the z-score and use the equation x = μ + (z * σ).

Step-by-step explanation:

To find the x value that corresponds to a given percentile of the normal distribution, we first need to calculate the z-score. The z-score represents the number of standard deviations a value is away from the mean. Once we have the z-score, we can use the equation x = μ + (z * σ) to find the x value. Let's say we want to find the x value that corresponds to the 90th percentile. First, we need to find the z-score that corresponds to the 90th percentile. In this case, the z-score is approximately 1.28. Now, substituting the values into the equation, we have x = μ + (1.28 * σ), where μ is the mean and σ is the standard deviation. This equation will give us the x value that corresponds to the 90th percentile.

Answer 2

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=(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]