Question

The heights of the peach trees in an orchard are normally distributed with a mean of 12.5 feet and a standard deviation of 1.8 feet.
What is the height of a peach tree with a z-score of −0.5 ?

Enter your answer, rounded to the nearest tenth _______ft

Answer 1

The height is 11.6 ft.

Z-scores are given by the formula

z=(X-μ)/σ

which in this situation leads us to

-0.5=(X-12.5)/1.8

Multiply both sides by 1.8:
-0.5(1.8) = ((X-12.5)/1.8)*1.8
-0.9 = X-12.5

Add 12.5 to both sides:
-0.9+12.5=X-12.5+12.5
11.6=X