Answer: the answer that i got was -11
Supposing a normal distribution, we find that:
The diameter of the smallest tree that is an outlier is of 16.36 inches.
--------------------------------
We suppose that tree diameters are normally distributed with <u>mean 8.8 inches and standard deviation 2.8 inches.</u>
<u />
In a normal distribution with mean
and standard deviation
, the z-score of a measure X is given by:
- The Z-score measures how many standard deviations the measure is from the mean.
- After finding the z-score, we look at the z-score table and find the p-value associated with this z-score, which is the percentile of X.<u>
</u>
<u />
In this problem:
- Mean of 8.8 inches, thus
. - Standard deviation of 2.8 inches, thus
.
<u />
The interquartile range(IQR) is the difference between the 75th and the 25th percentile.
<u />
25th percentile:
- X when Z has a p-value of 0.25, so X when Z = -0.675.
![Z = \frac{X - \mu}{\sigma}](https://tex.z-dn.net/?f=Z%20%3D%20%5Cfrac%7BX%20-%20%5Cmu%7D%7B%5Csigma%7D)
![-0.675 = \frac{X - 8.8}{2.8}](https://tex.z-dn.net/?f=-0.675%20%3D%20%5Cfrac%7BX%20-%208.8%7D%7B2.8%7D)
![X - 8.8 = -0.675(2.8)](https://tex.z-dn.net/?f=X%20-%208.8%20%3D%20-0.675%282.8%29)
![X = 6.91](https://tex.z-dn.net/?f=X%20%3D%206.91)
75th percentile:
- X when Z has a p-value of 0.75, so X when Z = 0.675.
![Z = \frac{X - \mu}{\sigma}](https://tex.z-dn.net/?f=Z%20%3D%20%5Cfrac%7BX%20-%20%5Cmu%7D%7B%5Csigma%7D)
![0.675 = \frac{X - 8.8}{2.8}](https://tex.z-dn.net/?f=0.675%20%3D%20%5Cfrac%7BX%20-%208.8%7D%7B2.8%7D)
![X - 8.8 = 0.675(2.8)](https://tex.z-dn.net/?f=X%20-%208.8%20%3D%200.675%282.8%29)
![X = 10.69](https://tex.z-dn.net/?f=X%20%3D%2010.69)
The IQR is:
![IQR = 10.69 - 6.91 = 3.78](https://tex.z-dn.net/?f=IQR%20%3D%2010.69%20-%206.91%20%3D%203.78)
What is the diameter, in inches, of the smallest tree that is an outlier?
- The diameter is <u>1.5IQR above the 75th percentile</u>, thus:
![10.69 + 1.5(3.78) = 16.36](https://tex.z-dn.net/?f=10.69%20%2B%201.5%283.78%29%20%3D%2016.36)
The diameter of the smallest tree that is an outlier is of 16.36 inches.
<u />
A similar problem is given at brainly.com/question/15683591
Id say 40%
because 8 are math so 9 of them are other
Answer:
87.08% percentage of families spend more than $4000 annually on food and drink
Step-by-step explanation:
Given -
average annual expenditure on food and drink for all families is $5700
Mean
= 5700
standard deviation
= 1500
Let X be the no of families spend annually on food and drink
percentage of families spend more than $4000 annually on food and drink =
= ![P(\frac{X - \nu }{\sigma }> \frac{ 4000 - 5700}{1500})](https://tex.z-dn.net/?f=P%28%5Cfrac%7BX%20-%20%5Cnu%20%7D%7B%5Csigma%20%7D%3E%20%5Cfrac%7B%204000%20-%205700%7D%7B1500%7D%29)
=
Using ![(Z = \frac{X - \nu }{\sigma })](https://tex.z-dn.net/?f=%28Z%20%3D%20%5Cfrac%7BX%20-%20%5Cnu%20%7D%7B%5Csigma%20%7D%29)
= 1 - ![P(Z](https://tex.z-dn.net/?f=P%28Z%20%3C-%201.13%29)
= 1 - .1292
= .8708
= 87.08%
So basically the height is divided by a certain number to evenly divide it