What is the z-score

Question

the number of nuts in a can of mixed nuts is found to be normally distributed, with a mean of 500 nuts and standard deviation of 20 nuts. my can of mixed nuts has only 475 nuts. what is the z-score for this can of nuts?

Answer 1

use the formula z = (x - μ / σ  where mu (μ) is the mean and sigma (σ) is the standard deviation.

Answer 2

z = (475 - 500)/20 = -25/20 = -1.25

 

That is, 475 is 1.25 standard deviations below the mean.