The heights of a certain type of tree are approximately normally distributed with a mean height y = 5 ft and a standard deviation = 0.4 ft. Which statement must be true? O A tre…

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asked Jan 1, 2020 146k views

2 Answers

Radu Caprescu · Answer 1 · 2020-01-06T20:07:20+0000

Answer: Fourth Option:

"A tree with a height of 6.2 ft is 3 standard deviations above the mean"

Explanation:

It is said that an X value is found Z standard deviations from the mean mu if:

$(X-\mu)/(\sigma) = Z$

In this case we have that:

$\mu=5\ ft$

$\sigma=0.4\ ft$

We have four different values of X and we must calculate the Z-score for each

For
$X =5.4\ ft$

$Z=(X-\mu)/(\sigma)$

Z=(5.4-5)/(0.4)=1

This means that: A tree with a height of 5.4 ft is 1 standard deviation above the mean

First Option: False

For
$X =4.6\ ft$

$Z=(X-\mu)/(\sigma)$

Z=(4.6-5)/(0.4)=-1

This means that: A tree with a height of 4.6 ft is 1 standard deviation below the mean

Second Option: False

For
$X =5.8\ ft$

$Z=(X-\mu)/(\sigma)$

Z=(5.8-5)/(0.4)=2

This means that: A tree with a height of 5.8 ft is 2 standard deviation above the mean

Third Option: False

For
$X =6.2\ ft$

$Z=(X-\mu)/(\sigma)$

Z=(6.2-5)/(0.4)=3

This means that: A tree with a height of 6.2 ft is 3 standard deviations above the mean.

Fourth Option: True