<h2><em>a) </em><u>The z-value associated with 25.0</u></h2><h2>Z =
1.25</h2><h2 /><h2><em>b)</em> <u>proportion of the population is between 20.0 and 25.0 is</u></h2><h2>Proportion =
0.3944</h2><h2 /><h2><em>c)</em> <u>proportion of the population is less than 18.0 is</u></h2><h2>Proportion =
0.3085</h2>
Calculations:
Normal pop has mean of 20.0
standard deviation = 4.0
XNN(20.0, 4.0)
a).
![z=\frac{x-h}{z}](https://tex.z-dn.net/?f=z%3D%5Cfrac%7Bx-h%7D%7Bz%7D)
![=\frac{25-20}{4.0} =\frac{5}{4} =1.25](https://tex.z-dn.net/?f=%3D%5Cfrac%7B25-20%7D%7B4.0%7D%20%3D%5Cfrac%7B5%7D%7B4%7D%20%3D1.25)
<u>Z = 1.25</u>
<u></u>
b).
The proportion between 20 and 25 is P(20 <x<25.0)
![=p(\frac{20-20}{4} < z < \frac{25-0}{4} )](https://tex.z-dn.net/?f=%3Dp%28%5Cfrac%7B20-20%7D%7B4%7D%20%3C%20z%20%3C%20%5Cfrac%7B25-0%7D%7B4%7D%20%29)
![=P(0 < z < 1.25)](https://tex.z-dn.net/?f=%3DP%280%20%3C%20z%20%3C%201.25%29)
![=P(Z < 1.25)-P(z < 0)](https://tex.z-dn.net/?f=%3DP%28Z%20%3C%201.25%29-P%28z%20%3C%200%29)
![=0.8944-0.5000](https://tex.z-dn.net/?f=%3D0.8944-0.5000)
P(20 < x < 25)=0.3944
c).
The proportion value is less than 18 when
![P(x < 18)=p(\frac{x--4}{6} < \frac{18-20}{4}](https://tex.z-dn.net/?f=P%28x%20%3C%2018%29%3Dp%28%5Cfrac%7Bx--4%7D%7B6%7D%20%3C%20%5Cfrac%7B18-20%7D%7B4%7D)
![=P(z < \frac{-2}{4})](https://tex.z-dn.net/?f=%3DP%28z%20%3C%20%5Cfrac%7B-2%7D%7B4%7D%29)
![=P(z < -0.5)](https://tex.z-dn.net/?f=%3DP%28z%20%3C%20-0.5%29)
P(x<18) = 0.3085
Answer:
See below
Step-by-step explanation:
we have f(x) = -(x-7) + 3
and we want to find f(4)
essentially, f(4) means that the input is 4 and to find the output we plug in the value of the input where ever x is and evaluate.
So for f(x) = -(x-7) + 3
To find f(4) we replace all x's with 4
f(4) = -(4-7) + 3
we now evaluate
==> subtract 7 from 4
f(4) = -(-3) + 3
==> apply two negative rule ( basically if there are two negative signs they cancel out and the number turn positive )
f(4) = 3 + 3
==> add 3 and 3
f(4) = 6
The box with the bunk bed will not fit in the mini van
Step-by-step explanation:
Step 1 :
Given
Length of the cuboid = 6 feet
Width of the cuboid = 2 feet
Height of the cuboid = 3 feet
The diagonal of the cuboid is
![\sqrt{l^{2}+w^{2}+h^{2}} = \sqrt{6^{2}+2^{2}+3^{2}}\\= \sqrt{49}](https://tex.z-dn.net/?f=%5Csqrt%7Bl%5E%7B2%7D%2Bw%5E%7B2%7D%2Bh%5E%7B2%7D%7D%20%3D%20%5Csqrt%7B6%5E%7B2%7D%2B2%5E%7B2%7D%2B3%5E%7B2%7D%7D%5C%5C%3D%20%5Csqrt%7B49%7D)
= 7 feet
Step 2 :
The utmost length of the diagonal of the box which the minivan can hold is 6.8 feet
The length of the diagonal of the box containing the bunk bed is 7 feet which is greater than 6.8 feet.
Hence the trunk of the mini van cannot hold the bunk bed
Equal steps mean each number is the same distance from the previous one
From -2 to 28 is 28 units
There are 4 spaces between the numbers
28/4 = 7
Each number is in increase of 7
-2 + 7 = 5
5+7 = 12
12+7 = 19
19+7 = 26
The third number would be 12