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:
[tex]\frac{X-\mu}{\sigma} = Z[/tex]
In this case we have that:
[tex]\mu=5\ ft[/tex]
[tex]\sigma=0.4\ ft[/tex]
We have four different values of X and we must calculate the Z-score for each
For [tex]X =5.4\ ft[/tex]
[tex]Z=\frac{X-\mu}{\sigma}[/tex]
[tex]Z=\frac{5.4-5}{0.4}=1[/tex]
This means that: A tree with a height of 5.4 ft is 1 standard deviation above the mean
First Option: False
For [tex]X =4.6\ ft[/tex]
[tex]Z=\frac{X-\mu}{\sigma}[/tex]
[tex]Z=\frac{4.6-5}{0.4}=-1[/tex]
This means that: A tree with a height of 4.6 ft is 1 standard deviation below the mean
Second Option: False
For [tex]X =5.8\ ft[/tex]
[tex]Z=\frac{X-\mu}{\sigma}[/tex]
[tex]Z=\frac{5.8-5}{0.4}=2[/tex]
This means that: A tree with a height of 5.8 ft is 2 standard deviation above the mean
Third Option: False
For [tex]X =6.2\ ft[/tex]
[tex]Z=\frac{X-\mu}{\sigma}[/tex]
[tex]Z=\frac{6.2-5}{0.4}=3[/tex]
This means that: A tree with a height of 6.2 ft is 3 standard deviations above the mean.
Fourth Option: True
