Answer:
The 99% confidence interval for the percentage of people who own a tablet computer is between 71.59% and 88.41%
Step-by-step explanation:
Confidence interval for the proportion of people who own a tablet:
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 = 150, \pi = \frac{120}{150} = 0.8](https://tex.z-dn.net/?f=n%20%3D%20150%2C%20%5Cpi%20%3D%20%5Cfrac%7B120%7D%7B150%7D%20%3D%200.8)
99% 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}} = 0.8 - 2.575\sqrt{\frac{0.8*0.2}{150}} = 0.7159](https://tex.z-dn.net/?f=%5Cpi%20-%20z%5Csqrt%7B%5Cfrac%7B%5Cpi%281-%5Cpi%29%7D%7Bn%7D%7D%20%3D%200.8%20-%202.575%5Csqrt%7B%5Cfrac%7B0.8%2A0.2%7D%7B150%7D%7D%20%3D%200.7159)
The upper limit of this interval is:
![\pi + z\sqrt{\frac{\pi(1-\pi)}{n}} = 0.8 + 2.575\sqrt{\frac{0.8*0.2}{150}} = 0.8841](https://tex.z-dn.net/?f=%5Cpi%20%2B%20z%5Csqrt%7B%5Cfrac%7B%5Cpi%281-%5Cpi%29%7D%7Bn%7D%7D%20%3D%200.8%20%2B%202.575%5Csqrt%7B%5Cfrac%7B0.8%2A0.2%7D%7B150%7D%7D%20%3D%200.8841)
Percentage:
Multiply the proportion by 100.
0.7159*100 = 71.59%
0.8841*100 = 88.41%
The 99% confidence interval for the percentage of people who own a tablet computer is between 71.59% and 88.41%
Good morning,
Answer:
<h2>r = 4 cm</h2>
Step-by-step explanation:
V = h × (base area)
= 12 × (π×r²)
then 192π = 12π×r²
Then 192 = 12×r²
Then r² = 192÷12 = 16
Then r = √16 = 4.
:)
Plotting the points could help you notice that they lie along a parabola. In particular, you can see that
is always 4 more than
.
So, the relation is
![y=x^2+4](https://tex.z-dn.net/?f=y%3Dx%5E2%2B4)
![\bf x=1-y\implies x+y=1\implies y=-x+1\\\\ -------------------------------\\\\ 2+y=x+1\implies y=x+1-2\implies y=x-1](https://tex.z-dn.net/?f=%5Cbf%20x%3D1-y%5Cimplies%20x%2By%3D1%5Cimplies%20y%3D-x%2B1%5C%5C%5C%5C%0A-------------------------------%5C%5C%5C%5C%0A2%2By%3Dx%2B1%5Cimplies%20y%3Dx%2B1-2%5Cimplies%20y%3Dx-1)
notice the equations in slope-intercept form, the first one has a slope of -1, the second one has a slope of 1.
if the slopes are equal, and the constant is different, they lines are parallel.
if the slopes are equal, and the constant is the same the equations are exactly the same thing, and the lines are coincident, on slapped on top of the other.
if the slopes differ, like here, then they have a solution, where they
intersect.