In a distribution with a standard deviation of eight, an individual score of 42 corresponds to a Z score of -0.5. What is the mean of this distribution?

Question

Statistics

Answer 1

Hello, thank you for taking the time to post your question!

The underlying equation that you want to use here is that

Z = (x – mean) / standard deviation

Plugging in the values that we know gives

-0.5 = (42 – mean) / 8

Then we want to solve for the value of the “mean” algebraically

-0.5(8) = 42 – mean

-4 = 42 – mean

Mean = 46

I hope that helps get you moving in the right direction! Feel free to reach out if you have any additional questions beyond that :)

Answer 2

Shay:

 

The z_score is z = (individual score - mean)/std_dev.

 

Using the info given, -0.5 = (42 - mean)/ 8.

 

-4 = 42 - mean

 

mean = 38.  Done.

 

Dattaprabhakar (Dr. G.)