Answer:
He must survey 123 adults.
Step-by-step explanation:
In a sample with a number n of people surveyed with a probability of a success of
, and a confidence level of
, we have the following confidence interval of proportions.
In which
z is the z-score that has a p-value of
.
The margin of error is:
![M = z\sqrt{\frac{\pi(1-\pi)}{n}}](https://tex.z-dn.net/?f=M%20%3D%20z%5Csqrt%7B%5Cfrac%7B%5Cpi%281-%5Cpi%29%7D%7Bn%7D%7D)
Assume that a recent survey suggests that about 87% of adults have heard of the brand.
This means that ![\pi = 0.87](https://tex.z-dn.net/?f=%5Cpi%20%3D%200.87)
90% confidence level
So
, z is the value of Z that has a p-value of
, so
.
How many adults must he survey in order to be 90% confident that his estimate is within five percentage points of the true population percentage?
This is n for which M = 0.05. So
![M = z\sqrt{\frac{\pi(1-\pi)}{n}}](https://tex.z-dn.net/?f=M%20%3D%20z%5Csqrt%7B%5Cfrac%7B%5Cpi%281-%5Cpi%29%7D%7Bn%7D%7D)
![0.05 = 1.645\sqrt{\frac{0.87*0.13}{n}}](https://tex.z-dn.net/?f=0.05%20%3D%201.645%5Csqrt%7B%5Cfrac%7B0.87%2A0.13%7D%7Bn%7D%7D)
![0.05\sqrt{n} = 1.645\sqrt{0.87*0.13}](https://tex.z-dn.net/?f=0.05%5Csqrt%7Bn%7D%20%3D%201.645%5Csqrt%7B0.87%2A0.13%7D)
![\sqrt{n} = \frac{1.645\sqrt{0.87*0.13}}{0.05}](https://tex.z-dn.net/?f=%5Csqrt%7Bn%7D%20%3D%20%5Cfrac%7B1.645%5Csqrt%7B0.87%2A0.13%7D%7D%7B0.05%7D)
![(\sqrt{n})^2 = (\frac{1.645\sqrt{0.87*0.13}}{0.05})^2](https://tex.z-dn.net/?f=%28%5Csqrt%7Bn%7D%29%5E2%20%3D%20%28%5Cfrac%7B1.645%5Csqrt%7B0.87%2A0.13%7D%7D%7B0.05%7D%29%5E2)
![n = 122.4](https://tex.z-dn.net/?f=n%20%3D%20122.4)
Rounding up:
He must survey 123 adults.
Answer:
90 degrees is a right angle.
Step-by-step explanation:
|_
^ That would be a 90 degrees angle.
|
|
|____
|___|____________
Imagine this is a graph, that little square of the right would represent 90 degrees.
Angles less than 90 are acute angles, angles over 90 but under 180 degrees would be obtuse, and angles that are equal to 180 degrees are straight.
Answer:118.3
Step-by-step explanation:
=0.5*13*18.2
I could help you, but how many paper clips were there? divide 7.20 by whatever number it is...
B is the correct answer because 1 gallon of gas is 1.05 dollars, so 15 × 1.05 is 15.75...