Opposite sides are congruent and have the same slope.
Answer:
The 80% confidence interval for the population proportion of disks which are defective is (0.059, 0.079).
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
.
Suppose a sample of 1067 floppy disks is drawn. Of these disks, 74 were defective.
This means that ![n = 1067, \pi = \frac{74}{1067} = 0.069](https://tex.z-dn.net/?f=n%20%3D%201067%2C%20%5Cpi%20%3D%20%5Cfrac%7B74%7D%7B1067%7D%20%3D%200.069)
80% 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}} = 0.069 - 1.28\sqrt{\frac{0.069*0.931}{1067}} = 0.059](https://tex.z-dn.net/?f=%5Cpi%20-%20z%5Csqrt%7B%5Cfrac%7B%5Cpi%281-%5Cpi%29%7D%7Bn%7D%7D%20%3D%200.069%20-%201.28%5Csqrt%7B%5Cfrac%7B0.069%2A0.931%7D%7B1067%7D%7D%20%3D%200.059)
The upper limit of this interval is:
![\pi + z\sqrt{\frac{\pi(1-\pi)}{n}} = 0.069 + 1.28\sqrt{\frac{0.069*0.931}{1067}} = 0.079](https://tex.z-dn.net/?f=%5Cpi%20%2B%20z%5Csqrt%7B%5Cfrac%7B%5Cpi%281-%5Cpi%29%7D%7Bn%7D%7D%20%3D%200.069%20%2B%201.28%5Csqrt%7B%5Cfrac%7B0.069%2A0.931%7D%7B1067%7D%7D%20%3D%200.079)
The 80% confidence interval for the population proportion of disks which are defective is (0.059, 0.079).
Answer: simply, solve for it ! .
Like-if you have an equation with 2 sides , you have to flip its sign and hand on (whatever you have ) to the against side .
The width that Mason should set his compass when constructing segment FG is: A. The distance from B to E.
<h3>Width</h3>
FG should be congruent to segment BE. Based on this Mason should set his compass to the width of segment BE when Mason is constructing segment FG.
Hence, the width that Mason should set his compass when constructing segment FG is the distance from B to E which is option is A.
Learn more about width here:brainly.com/question/25855344
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![\cos(2x) + {sin}^{2}(x) =](https://tex.z-dn.net/?f=%20%5Ccos%282x%29%20%20%2B%20%20%7Bsin%7D%5E%7B2%7D%28x%29%20%3D%20%20)
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![\cos(2x) = {cos}^{2}(x) - {sin}^{2}(x)](https://tex.z-dn.net/?f=%20%5Ccos%282x%29%20%20%3D%20%20%7Bcos%7D%5E%7B2%7D%28x%29%20-%20%20%7Bsin%7D%5E%7B2%7D%28x%29%20%20)
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![{cos}^{2}(x) - {sin}^{2}(x) + {sin}^{2}(x) = \\](https://tex.z-dn.net/?f=%20%7Bcos%7D%5E%7B2%7D%28x%29%20-%20%20%7Bsin%7D%5E%7B2%7D%28x%29%20%2B%20%20%7Bsin%7D%5E%7B2%7D%28x%29%20%3D%20%20%5C%5C%20%20)
![{cos}^{2}(x) = 1 - {sin}^{2}(x)](https://tex.z-dn.net/?f=%20%7Bcos%7D%5E%7B2%7D%28x%29%20%20%3D%201%20-%20%20%7Bsin%7D%5E%7B2%7D%28x%29%20)
Thus the correct answer is (( A )) .
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