Answer:
The 95% confidence interval estimate for the true proportion of adults residents of this city who have cell phones is (0.81, 0.874).
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.
![\pi \pm z\sqrt{\frac{\pi(1-\pi)}{n}}](https://tex.z-dn.net/?f=%5Cpi%20%5Cpm%20z%5Csqrt%7B%5Cfrac%7B%5Cpi%281-%5Cpi%29%7D%7Bn%7D%7D)
In which
z is the zscore that has a pvalue of
.
For this problem, we have that:
![n = 500, \pi = \frac{421}{500} = 0.842](https://tex.z-dn.net/?f=n%20%3D%20500%2C%20%5Cpi%20%3D%20%5Cfrac%7B421%7D%7B500%7D%20%3D%200.842)
95% confidence level
So
, z is the value of Z that has a pvalue of
, so
.
The lower limit of this interval is:
![\pi - z\sqrt{\frac{\pi(1-\pi)}{n}} = 0.842 - 1.96\sqrt{\frac{0.842*0.158}{500}} = 0.81](https://tex.z-dn.net/?f=%5Cpi%20-%20z%5Csqrt%7B%5Cfrac%7B%5Cpi%281-%5Cpi%29%7D%7Bn%7D%7D%20%3D%200.842%20-%201.96%5Csqrt%7B%5Cfrac%7B0.842%2A0.158%7D%7B500%7D%7D%20%3D%200.81)
The upper limit of this interval is:
![\pi + z\sqrt{\frac{\pi(1-\pi)}{n}} = 0.842 + 1.96\sqrt{\frac{0.842*0.158}{500}} = 0.874](https://tex.z-dn.net/?f=%5Cpi%20%2B%20z%5Csqrt%7B%5Cfrac%7B%5Cpi%281-%5Cpi%29%7D%7Bn%7D%7D%20%3D%200.842%20%2B%201.96%5Csqrt%7B%5Cfrac%7B0.842%2A0.158%7D%7B500%7D%7D%20%3D%200.874)
The 95% confidence interval estimate for the true proportion of adults residents of this city who have cell phones is (0.81, 0.874).
Answer:
![y = \frac{1}{2} x + \frac{1}{2}](https://tex.z-dn.net/?f=y%20%3D%20%20%5Cfrac%7B1%7D%7B2%7D%20x%20%2B%20%20%5Cfrac%7B1%7D%7B2%7D%20)
Step-by-step explanation:
equation of line formula:
![y = mx + c](https://tex.z-dn.net/?f=y%20%3D%20mx%20%2B%20c)
m = slope
c = y-intercept
1) find m
slope formula:
![m = \frac{ y_{2} - y_{1} }{ x_{2} - x_{1}}](https://tex.z-dn.net/?f=m%20%3D%20%20%20%5Cfrac%7B%20y_%7B2%7D%20-%20%20y_%7B1%7D%20%7D%7B%20x_%7B2%7D%20-%20%20x_%7B1%7D%7D%20)
take 2 coordinates from the given graph and substitute the values into the slope formula
i) (-1,0)
![x _{1} = - 1](https://tex.z-dn.net/?f=x%20_%7B1%7D%20%3D%20%20-%201)
![y_{1} = 0](https://tex.z-dn.net/?f=y_%7B1%7D%20%3D%200)
ii) (3,2)
![x_{2} = 3](https://tex.z-dn.net/?f=x_%7B2%7D%20%3D%203)
![y_{2} = 2](https://tex.z-dn.net/?f=y_%7B2%7D%20%3D%202)
substitute the values into the slope formula
![m = \frac{2 - 0}{3 - ( - 1)}](https://tex.z-dn.net/?f=m%20%3D%20%20%5Cfrac%7B2%20-%200%7D%7B3%20-%20%28%20-%201%29%7D%20)
![m = \frac{2}{4}](https://tex.z-dn.net/?f=m%20%3D%20%20%5Cfrac%7B2%7D%7B4%7D%20)
![m = \frac{1}{2}](https://tex.z-dn.net/?f=m%20%3D%20%20%5Cfrac%7B1%7D%7B2%7D%20)
2) find the half equation of the line by substituting the value of m into the equation of line formula
![y = \frac{1}{2} x + c](https://tex.z-dn.net/?f=y%20%3D%20%20%5Cfrac%7B1%7D%7B2%7D%20x%20%2B%20c)
3) find c by substituting either coordinate into the half equation
(3,2)
x = 3
y = 2
![2 = \frac{1}{2} (3) + c](https://tex.z-dn.net/?f=2%20%3D%20%20%5Cfrac%7B1%7D%7B2%7D%20%283%29%20%2B%20c)
![2 = \frac{3}{2} + c](https://tex.z-dn.net/?f=2%20%3D%20%20%5Cfrac%7B3%7D%7B2%7D%20%20%2B%20c)
![2 - \frac{3}{2} = c](https://tex.z-dn.net/?f=2%20-%20%20%5Cfrac%7B3%7D%7B2%7D%20%20%3D%20c)
![\frac{1}{2} = c](https://tex.z-dn.net/?f=%20%5Cfrac%7B1%7D%7B2%7D%20%3D%20c%20)
![c = \frac{1}{2}](https://tex.z-dn.net/?f=c%20%3D%20%20%5Cfrac%7B1%7D%7B2%7D%20)
4) find equation of line by substituting the value of c into the half equation
![y = \frac{1}{2} x + \frac{1}{2}](https://tex.z-dn.net/?f=y%20%3D%20%20%5Cfrac%7B1%7D%7B2%7D%20x%20%2B%20%20%5Cfrac%7B1%7D%7B2%7D%20)
<u><em>*(Information)*=</em></u>
-This question is asking for a expression
- She has 16 photo on her phone (Since this is a number this is a constant)
-
is the variable
- Variables are unknown numbers
-Constants is a number like
and more
<u><em>*(Answer)*=</em></u> ![p+16](https://tex.z-dn.net/?f=p%2B16)
<u><em>*(Explanation)*=</em></u> Te reason why it is
is because p is the unknown number. The constant is 16 in this question.
Answer:
∑ₙ₌₁⁸ (3n − 9)
Step-by-step explanation:
This is an arithmetic series where the first term is -6 and the common difference is 3. The nth term can be written as:
aₙ = a₁ + d (n − 1)
aₙ = -6 + 3 (n − 1)
There are 8 terms in this series, so the sum is:
∑ₙ₌₁⁸ [-6 + 3 (n − 1)]
Simplified:
∑ₙ₌₁⁸ (3n − 9)