Question

The heights of a certain type of tree are approximately normally distributed with a mean height y = 5 ft and a standard

Answer 1

Answer: Fourth Option:

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

Step-by-step explanation:

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

$\frac{X-\mu}{\sigma} = Z$

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 $X =5.4\ ft$

$Z=\frac{X-\mu}{\sigma}$

$Z=\frac{5.4-5}{0.4}=1$

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

First Option: False

For $X =4.6\ ft$

$Z=\frac{X-\mu}{\sigma}$

$Z=\frac{4.6-5}{0.4}=-1$

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

Second Option: False

For $X =5.8\ ft$

$Z=\frac{X-\mu}{\sigma}$

$Z=\frac{5.8-5}{0.4}=2$

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

Third Option: False

For $X =6.2\ ft$

$Z=\frac{X-\mu}{\sigma}$

$Z=\frac{6.2-5}{0.4}=3$

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

Fourth Option: True

Answer 2

Answer:

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

Step-by-step explanation:

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