The set of life spans of an appliance is normally distributed with a mean mc013-1.jpg = 48 months and a standard deviation mc013-2.jpg = 8 months. What is the life span of an appliance that has a z-score of –3?

The life span would be 24 months.

The formula for z-scores is:
[tex]z=\frac{X-\mu}{\sigma}[/tex]

Using the information we're given we have:
[tex]-3=\frac{X-48}{8}[/tex]

Multiply both sides by 8 to cancel it:
-3(8) = ((X-48)/8)*8
-24 = X-48

Add 48 to both sides:
-24+48 = X-48+48
24=X