Using the normal distribution, it is found that:
1. 85% of NBA players are taller than Greg.
2. 15% are shorter.
3. A height of 6'11'' would be needed.
<h3>Normal Probability Distribution</h3>
In a normal distribution with mean
and standard deviation
, the z-score of a measure X is given by:
![Z = \frac{X - \mu}{\sigma}](https://tex.z-dn.net/?f=Z%20%3D%20%5Cfrac%7BX%20-%20%5Cmu%7D%7B%5Csigma%7D)
- It 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.
In this problem:
- In inches, considering that a feet has 12 inches, the mean is of
.
- The standard deviation is of
.
- Greg is 6'3'', that is, X = 6 x 12 + 3 = 75.
Item 1:
The proportion is <u>one subtracted by the p-value of Z</u>, hence:
![Z = \frac{X - \mu}{\sigma}](https://tex.z-dn.net/?f=Z%20%3D%20%5Cfrac%7BX%20-%20%5Cmu%7D%7B%5Csigma%7D)
![Z = \frac{75 - 79}{3.9}](https://tex.z-dn.net/?f=Z%20%3D%20%5Cfrac%7B75%20-%2079%7D%7B3.9%7D)
![Z = -1.03](https://tex.z-dn.net/?f=Z%20%3D%20-1.03)
has a p-value of 0.15
1 - 0.15 = 0.85.
85% of NBA players are taller than Greg.
Item 2:
100 - 85 = 15% are shorter.
Item 3:
This is X when Z has a p-value of 1 - 0.025 = 0.975, so X when Z = 1.96.
![Z = \frac{X - \mu}{\sigma}](https://tex.z-dn.net/?f=Z%20%3D%20%5Cfrac%7BX%20-%20%5Cmu%7D%7B%5Csigma%7D)
![1.96 = \frac{X - 75}{3.9}](https://tex.z-dn.net/?f=1.96%20%3D%20%5Cfrac%7BX%20-%2075%7D%7B3.9%7D)
![X - 75 = 1.96(3.9)](https://tex.z-dn.net/?f=X%20-%2075%20%3D%201.96%283.9%29)
![X = 83](https://tex.z-dn.net/?f=X%20%3D%2083)
83 = 6 x 12 + 11.
A height of 6'11'' would be needed.
More can be learned about the normal distribution at brainly.com/question/24663213
Answer:
(1/3) / 1.5 = x/3 solve for x.
x = 3*(1/3) /1.5 = 2 cups
Step-by-step explanation:
Answer:
y=-2/3 x +2
y=-x+2
Step-by-step explanation:
slope intercept form : y=mx+b
first find the slope :
two points from the graph : (0,2) (3,0)
y=b=2 when x=0 y = the constant b
m=(y2-y1)/(x2-x1)
m=0-2/3-0
m=-2/3
<h2>y=-2/3 x +2</h2>
question 26: two points from graph: (0,2),(1,1)
b=2 ( when x=0, y=b=2)
m=1-2/1-0
m=-1
<h2>y= - x+2</h2>
Answer:
the answer is 80 marbles in the sack.
Answer:
D
Step-by-step explanation:
according to the graph its shifting down
pls mark me brainliest