2(4z−2) = 44
Simplify both sides of the equation.
Distribute:
(2)(4z)+(2)(−2) = 44
8z + −4 = 44
8z − 4 = 44
Add 4 to both sides.
8z − 4 + 4 = 44 + 4
8z = 48
Divide both sides by 8
8z/8 48/8
z = 6
12.75+4.5+0.99+6.35= 12.75+4.5=17.25 .99+6.34=7.33 17.25+7.33= 24.58
$24.58
Answer:
The 92% confidence interval for the actual proportion of all office workers who are able to take every telephone call is (0.3676, 0.4324).
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 = 700, \pi = \frac{280}{700} = 0.4](https://tex.z-dn.net/?f=n%20%3D%20700%2C%20%5Cpi%20%3D%20%5Cfrac%7B280%7D%7B700%7D%20%3D%200.4)
92% 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}} = 0.4 - 1.75\sqrt{\frac{0.4*0.6}{700}} = 0.3676](https://tex.z-dn.net/?f=%5Cpi%20-%20z%5Csqrt%7B%5Cfrac%7B%5Cpi%281-%5Cpi%29%7D%7Bn%7D%7D%20%3D%200.4%20-%201.75%5Csqrt%7B%5Cfrac%7B0.4%2A0.6%7D%7B700%7D%7D%20%3D%200.3676)
The upper limit of this interval is:
![\pi + z\sqrt{\frac{\pi(1-\pi)}{n}} = 0.4 + 1.75\sqrt{\frac{0.4*0.6}{700}} = 0.4324](https://tex.z-dn.net/?f=%5Cpi%20%2B%20z%5Csqrt%7B%5Cfrac%7B%5Cpi%281-%5Cpi%29%7D%7Bn%7D%7D%20%3D%200.4%20%2B%201.75%5Csqrt%7B%5Cfrac%7B0.4%2A0.6%7D%7B700%7D%7D%20%3D%200.4324)
The 92% confidence interval for the actual proportion of all office workers who are able to take every telephone call is (0.3676, 0.4324).
Answer:
r = 4.908
Step-by-step explanation:
V = 885
height (given in the picture) = 11.7
V =
h
V = (3.14)(
)(h)
885 = (3.14)(
)(11.7)
885/3.14/11.7 = ![r^2](https://tex.z-dn.net/?f=r%5E2)
Take the square root and you get 4.908.