0.08*x+0.03*(29000-x)<span> </span>
Answer:
7 Caterpillars
Step-by-step explanation:
14/2
Using the z-distribution, a sample of 142,282 should be taken, which is not practical as it is too large of a sample.
<h3>What is a z-distribution confidence interval?</h3>
The confidence interval is:
![\overline{x} \pm z\frac{\sigma}{\sqrt{n}}](https://tex.z-dn.net/?f=%5Coverline%7Bx%7D%20%5Cpm%20z%5Cfrac%7B%5Csigma%7D%7B%5Csqrt%7Bn%7D%7D)
The margin of error is:
![M = z\frac{\sigma}{\sqrt{n}}](https://tex.z-dn.net/?f=M%20%3D%20z%5Cfrac%7B%5Csigma%7D%7B%5Csqrt%7Bn%7D%7D)
In which:
is the sample mean.
is the standard deviation for the population.
Assuming an uniform distribution, the standard deviation is given by:
![S = \sqrt{\frac{(4 - 0)^2}{12}} = 1.1547](https://tex.z-dn.net/?f=S%20%3D%20%5Csqrt%7B%5Cfrac%7B%284%20-%200%29%5E2%7D%7B12%7D%7D%20%3D%201.1547)
In this problem, we have a 95% confidence level, hence
, z is the value of Z that has a p-value of
, so the critical value is z = 1.96.
The sample size is found solving for n when the margin of error is of M = 0.006, hence:
![M = z\frac{\sigma}{\sqrt{n}}](https://tex.z-dn.net/?f=M%20%3D%20z%5Cfrac%7B%5Csigma%7D%7B%5Csqrt%7Bn%7D%7D)
![0.006 = 1.96\frac{1.1547}{\sqrt{n}}](https://tex.z-dn.net/?f=0.006%20%3D%201.96%5Cfrac%7B1.1547%7D%7B%5Csqrt%7Bn%7D%7D)
![0.006\sqrt{n} = 1.96 \times 1.1547](https://tex.z-dn.net/?f=0.006%5Csqrt%7Bn%7D%20%3D%201.96%20%5Ctimes%201.1547)
![\sqrt{n} = \frac{1.96 \times 1.1547}{0.006}](https://tex.z-dn.net/?f=%5Csqrt%7Bn%7D%20%3D%20%5Cfrac%7B1.96%20%5Ctimes%201.1547%7D%7B0.006%7D)
![(\sqrt{n})^2 = \left(\frac{1.96 \times 1.1547}{0.006}\right)^2](https://tex.z-dn.net/?f=%28%5Csqrt%7Bn%7D%29%5E2%20%3D%20%5Cleft%28%5Cfrac%7B1.96%20%5Ctimes%201.1547%7D%7B0.006%7D%5Cright%29%5E2)
n = 142,282.
A sample of 142,282 should be taken, which is not practical as it is too large of a sample.
More can be learned about the z-distribution at brainly.com/question/25890103
#SPJ1
Answer:
25
Step-by-step explanation:
180-90-65 = 25
Opposite angles are same