Q Cherry trees in a certain orchard have heights that are normally distributed w

Question

Q Cherry trees in a certain orchard have heights that are normally distributed with mean = 112 inches and standard deviation = 14 inches.

Find the 27th percentile of the tree heights.

    Find the 85th percentile of the tree heights.

Find the third quartile of the tree heights.

An agricultural scientist wants to study the tallest 1% of the trees to determine whether they have a certain gene that allows them to grow taller. To do this, she needs to study all the trees above a certain height. What height is this?

Explanation / Answer

Ans:

Given that

= 112 , = 14 inches

a)27th percentile means that

P(Z<=z)=0.27

z=-0.613

x=112-0.613*14=103.42

27th percentile =103.42

b)85th percentile means that

P(Z<=z)=0.85

z=1.036

x=112+1.036*14=126.5

85th percentile=126.5

c)Third quartile means that

P(Z<=z)=0.75

z=0.6745

x=112+0.6745*14=121.44

Third quartile=121.44

d)P(Z>=z)=0.01

P(Z<=z)=1-0.01=0.99

z=2.326

x=112+2.326*14=144.56

x=144.56

So,she needs to study all the trees above 144.56

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