The area is 18 units squared, I believe.
Answer:
a) ![z = 1.645](https://tex.z-dn.net/?f=z%20%3D%201.645)
b) The should sample at least 293 small claims.
Step-by-step explanation:
We have that to find our
level, that is the subtraction of 1 by the confidence interval divided by 2. So:
![\alpha = \frac{1-0.9}{2} = 0.05](https://tex.z-dn.net/?f=%5Calpha%20%3D%20%5Cfrac%7B1-0.9%7D%7B2%7D%20%3D%200.05)
Now, we have to find z in the Ztable as such z has a pvalue of
.
So it is z with a pvalue of
, so
, which means that the answer of question a is z = 1.645.
Now, find the margin of error M as such
![M = z*\frac{\sigma}{\sqrt{n}}](https://tex.z-dn.net/?f=M%20%3D%20z%2A%5Cfrac%7B%5Csigma%7D%7B%5Csqrt%7Bn%7D%7D)
In which
is the standard deviation of the population and n is the size of the sample.
(b) If the group wants their estimate to have a maximum error of $12, how many small claims should they sample?
They should sample at least n small claims, in which n is found when
. So
![M = z*\frac{\sigma}{\sqrt{n}}](https://tex.z-dn.net/?f=M%20%3D%20z%2A%5Cfrac%7B%5Csigma%7D%7B%5Csqrt%7Bn%7D%7D)
![12 = 1.645*\frac{124.88}{\sqrt{n}}](https://tex.z-dn.net/?f=12%20%3D%201.645%2A%5Cfrac%7B124.88%7D%7B%5Csqrt%7Bn%7D%7D)
![12\sqrt{n} = 205.43](https://tex.z-dn.net/?f=12%5Csqrt%7Bn%7D%20%3D%20205.43)
![\sqrt{n} = \frac{205.43}{12}](https://tex.z-dn.net/?f=%5Csqrt%7Bn%7D%20%3D%20%5Cfrac%7B205.43%7D%7B12%7D)
![\sqrt{n} = 17.12](https://tex.z-dn.net/?f=%5Csqrt%7Bn%7D%20%3D%2017.12)
![\sqrt{n}^{2} = (17.12)^{2}](https://tex.z-dn.net/?f=%5Csqrt%7Bn%7D%5E%7B2%7D%20%3D%20%2817.12%29%5E%7B2%7D)
![n = 293](https://tex.z-dn.net/?f=n%20%3D%20293)
The should sample at least 293 small claims.
It would be 3 hours. This is 3 hours because the problem says that daniel takes 9 hours to clean and office building and mark takes 6 hours so if you subtract 9hours from 6 hours it would be 3 hours total. Now this can be 2 answers it can also be 15 hours if you were to add 9 hours to 6 hours.
Setup Fee= $5,500Per CD Charge= $1.00Desired Cost Per CD= $3.50
x= number of CDs
Desired Cost Per CD= Cost per CD + Setup Fee
($3.50 * x)= ($1.00 * x) + $5,500multiply inside parentheses
$3.50x= $1.00x + $5,500subtract $1.00x from both sides
$2.50x= $5,500divide both sides by $2.50
x= 2,200 CDs
ANSWER: x= 2,200 CDs
Hope this helps! :)