Can someone check this

Question

Which description of normal distributions is correct (select all that apply)?

a. Normal distributions have a mean of zero and standard deviation of one.

b. Normal distributions can differ in their means, but their standard deviations must be the same.

c. Standard normal distributions cannot differ in both their means and their standard deviations.

d. Normal distributions cannot differ in their means, but can differ in their standard deviations.

e. None of the above are correct

 

Wouldn't this just be E since normal distributions can differ in their means and in their standard deviations.

Answer 1

Normal distributions can differ in their means and standard deviations. Additionally, standard normal distributions cannot differ in either their mean or standard deviation.

 

Normal distributions can have different means calculated from the given sample or population set. The standard deviation describes the spread of the data using the mean in its calculation, so the standard deviations of data normally distributed do not necessarily have to be the same either.   

 

The data from the normal distribution can be standardized by converting it to a z-score:

 

z = (x-µ)/σ

 

This gives the standard normal distribution, which always has a mean of 0 and a standard deviation of 1.  

 

I hope this helps!