Answer:
Your correct answer would be option 2. y = IxI -1 Please vote Brainliest!
Step-by-step explanation:
Using the z-distribution, we have that:
a) The 90% confidence interval for the proportion of all U.S. adults who could name all three branches of government is (0.339, 0.381). It means that we are 90% sure that the true population proportion is within these values.
b) The entire confidence interval is below 50%, which means that it provides convincing evidence that less than half of all U.S. adults could name all three branches of government.
<h3>What is a confidence interval of proportions?</h3>
A confidence interval of proportions is given by:
![\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:
is the sample proportion.
Item a:
For the parameters, we have that:
- 36% of adults in the United States could name all three branches of government, hence
.
- Sample of 1416 adults, hence
.
- 90% confidence level, hence
, z is the value of Z that has a p-value of
, so
.
The lower limit of this interval is:
![\pi - z\sqrt{\frac{\pi(1-\pi)}{n}} = 0.36 - 1.645\sqrt{\frac{0.36(0.64)}{1416}} = 0.339](https://tex.z-dn.net/?f=%5Cpi%20-%20z%5Csqrt%7B%5Cfrac%7B%5Cpi%281-%5Cpi%29%7D%7Bn%7D%7D%20%3D%200.36%20-%201.645%5Csqrt%7B%5Cfrac%7B0.36%280.64%29%7D%7B1416%7D%7D%20%3D%200.339)
The upper limit of this interval is:
![\pi + z\sqrt{\frac{\pi(1-\pi)}{n}} = 0.36 + 1.645\sqrt{\frac{0.36(0.64)}{1416}} = 0.381](https://tex.z-dn.net/?f=%5Cpi%20%2B%20z%5Csqrt%7B%5Cfrac%7B%5Cpi%281-%5Cpi%29%7D%7Bn%7D%7D%20%3D%200.36%20%2B%201.645%5Csqrt%7B%5Cfrac%7B0.36%280.64%29%7D%7B1416%7D%7D%20%3D%200.381)
The 90% confidence interval for the proportion of all U.S. adults who could name all three branches of government is (0.339, 0.381). It means that we are 90% sure that the true population proportion is within these values.
Item b:
The entire confidence interval is below 50%, which means that it provides convincing evidence that less than half of all U.S. adults could name all three branches of government.
More can be learned about the z-distribution at brainly.com/question/15850972
Answer:
x = 128°
Step-by-step explanation:
123 + 109 + x = 360
x = 360 - (123 + 109)
x = 360 - 232
x = 128°