Question

The scores on a standardized test are normally distributed with a mean of 105 and standard deviation of 20. What test score is 1.8 standard deviations below the mean?

Answer 1

score = 69

Explanation:

to work this out we use the formula z = (x - υ) / σ

where z is the z-score, x is the observed value, υ is the mean and σ is the standard deviation.

1.8 standard deviations below mean means -1.8

z= (x - υ) / σ

-1.8 = (x - 105) / 20

-1.8 (20) = x - 105

-36 = x - 105

x = -36 + 105

= 69

our test score 1.8 standard deviations below the mean is 69