Describe how you can transform a nonstandard normal distribution to the standard normal distribution

Suppose X is your nonstandard normal distribution, with mean m and standard deviation s.

First, shift the mean to 0 by subtracting the mean m:

X - m

Then rescale your standard deviation by dividing by s:

(X - m) / s

This will be a standard normal distribution now (i.e. mean 0 and std. dev. 1)

The standard normal distribution is a normal distribution with a mean of 0 and a standard deviation of 1. Normal distributions can be transformed to standard normal distributions by the formula:

z = X- µ / σ

Where X is a score from the original normal distribution, μ is the mean of the original normal distribution, and σ is the standard deviation of the original normal distribution. The standard normal distribution is sometimes called the z distribution. A z score always reflects the number of standard deviations above or below the mean a particular score is. For instance, if a person scored a 70 on a test with a mean of 50 and a standard deviation of 10, then they scored 2 standard deviations above the mean. Converting the test scores to z scores, an X of 70 would be:

z = 70-50 / 10  = 2

So, a z score of 2 means the original score was 2 standard deviations above the mean. Note that the z distribution will only be a normal distribution if the original distribution (X) is normal.

A.

Step-by-step explanation:

the square root of 6 is roughly 1.57

so that means the ordered pair would read (2,1.57).

if you were to plot that point it would be on the circle.

Also the distance from the origin (0,0) to (3,0) is 3 units