Question

Pine trees and juniper trees are common to the San Bernardino

mountains. Pine trees have a mean height of 52 meters with a

standard deviation of 3 meters. Juniper trees have a mean

height of 22 meters with a standard deviation of 5 meters.

(a) At the base of a trail, there is a 48-meter-tall pine tree and a

33-meter-tall juniper tree. Calculate the Z-score for each of

these trees.

If necessary, round your answers to the nearest 2 decimal

places. Write both answers in the text box below.

Answer 1

Z-score = 0.9450

Explanation:

Step(i):-

mean height of pine tree (x₁⁻) = 52

standard deviation of pine tree σ₁ = 3

Mean height of Jupiter tree ((x₂⁻) = 22

standard deviation of Jupiter tree σ₂ = 5

Size of first sample n₁ = 48

size of second sample n₂ = 33

Step(ii):-

Z-score

`Z = \frac{x^(-) _(1) -x^(-) _(2) }{\sqrt{(S.D^(2) )/(n_(1) )+(S.D^(2) )/(n_(2) )} }`

`Z = \frac{52 -22 }{\sqrt{(3^(2) )/(48 )+(5^(2) )/(33 )} }`

Z = 0.9450