Question

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 tree with a height of 5.4 ft is 1 standard deviation below the mean
A tree with a height of 4.6 ft is 1 standard deviation above the mean.
A tree with a height of 5.8 ft is 2.5 standard deviations above the mean
A tree with a height of 6.2 ft is 3 standard deviations above the mean.

Answer 1

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

Explanation:

edge2020

Answer 2

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