Question

Tree heights: Cherry trees in a certain orchard have heights that are normally distributed with mean - 114 inches and standard deviation - 14 inches. Use the TI-84 PLUS calculator to answer the following. Round the answers to at least two decimals. (a) Find the 28" percentile of the tree heights. (b) Find the 84 percentile of the tree heights. (c) Find the third quartile of the tree heights. (d) 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? Part: 0/4 Part 1 of 4 Find the 28 percentile of the tree heights The 28 percentile of tree heights is inches.

Answer 1

X: heights of cherry trees.

X ~ N (114 , 14)

a). the 28 th percentile of tree height is = 105.84 inches

[ steps in ti 84 plus :-

2ND $\rightarrow$ vars $\rightarrow$ select invNorm $\rightarrow$ in area type 0.28 , in $\mu$ = 114 , in $\sigma$ = 14 $\rightarrow$ enter $\rightarrow$ enter.

you will get = 105.840219.

$P(X<x)=0.28$

$\Rightarrow x=105.84$ ]

b). the 84 th percentile of tree height is = 127.92 inches

[ steps in ti 84 plus :-

2ND $\rightarrow$ vars $\rightarrow$ select invNorm $\rightarrow$ in area type 0.84 , in $\mu$ = 114 , in $\sigma$ = 14 $\rightarrow$ enter $\rightarrow$ enter.

you will get = 127.9224105

$P(X<x)=0.84$

$\Rightarrow x=127.92$ ]

c). the third quartile of the tree heights = 123.44 inches.

[ steps in ti 84 plus :-

2ND $\rightarrow$ vars $\rightarrow$ select invNorm $\rightarrow$ in area type 0.75 , in $\mu$ = 114 , in $\sigma$ = 14 $\rightarrow$ enter $\rightarrow$ enter.

you will get = 123.4428565

$P(X<x)=0.75$ [ third quartile = 3/4 = 0.75 ]

$\Rightarrow x=123.44$ ]

d). the height above which the tallest 1 % of tree lie = 146.57 inches

[ steps in ti 84 plus :-

2ND $\rightarrow$ vars $\rightarrow$ select invNorm $\rightarrow$ in area type 0.99 , in $\mu$ = 114 , in $\sigma$ = 14 $\rightarrow$ enter $\rightarrow$ enter.

you will get = 146.5688703

$P(X>x)=0.01$

$\Rightarrow P(X<x)=1-0.01=0.99$

$\Rightarrow x=146.57$ ]

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