Question

Cherry trees in a certain orchard have heights that are normally distributed with mean μ = 109 inches and standard deviation σ = 11 inches. Use the Cumulative Normal Distribution Table to answer the following.

(a) Find the 23 rd percentile of the tree heights.

(b) Find the 81 st percentile of the tree heights.

(c) Find the second quartile of the tree heights.

(d) An agricultural scientist wants to study the tallest 2 % 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?

Answer 1

u	109
sd	11

a) Answer: 100.8727

Percent	0.23
alpha	0.77
z=normsinv(alpha)	-0.73885
x=z*standard deviation+u	100.8727

b) Answer: 118.6569

Percent	0.81
alpha	0.19
z=normsinv(alpha)	0.877896
x=z*standard deviation+u	118.6569

c) Answer: 109

Percent	0.5
alpha	0.5
z=normsinv(alpha)	0
x=z*standard deviation+u	109

d) Answer: 131.5912

Percent	0.98
alpha	0.02
z=normsinv(alpha)	2.053749
x=z*standard deviation+u	131.5912