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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.

Respuesta :

Answer:

Z-score = 0.9450

Step-by-step 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

               [tex]Z = \frac{x^{-} _{1} -x^{-} _{2} }{\sqrt{\frac{S.D^{2} }{n_{1} }+\frac{S.D^{2} }{n_{2} }} }[/tex]

              [tex]Z = \frac{52 -22 }{\sqrt{\frac{3^{2} }{48 }+\frac{5^{2} }{33 }} }[/tex]

             Z = 0.9450

             

             

             

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