Using the z-distribution, as we have a proportion, the 95% confidence interval is (0.2316, 0.3112).
<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.
In this problem, we have a 95% confidence level, hence
, z is the value of Z that has a p-value of
, so the critical value is z = 1.96.
We also consider that 130 out of the 479 season ticket holders spent $1000 or more at the previous two home football games, hence:
![n = 479, \pi = \frac{130}{479} = 0.2714](https://tex.z-dn.net/?f=n%20%3D%20479%2C%20%5Cpi%20%3D%20%5Cfrac%7B130%7D%7B479%7D%20%3D%200.2714)
Hence the bounds of the interval are found as follows:
![\pi - z\sqrt{\frac{\pi(1-\pi)}{n}} = 0.2714 - 1.96\sqrt{\frac{0.2714(0.7286)}{479}} = 0.2316](https://tex.z-dn.net/?f=%5Cpi%20-%20z%5Csqrt%7B%5Cfrac%7B%5Cpi%281-%5Cpi%29%7D%7Bn%7D%7D%20%3D%200.2714%20-%201.96%5Csqrt%7B%5Cfrac%7B0.2714%280.7286%29%7D%7B479%7D%7D%20%3D%200.2316)
![\pi + z\sqrt{\frac{\pi(1-\pi)}{n}} = 0.2714 + 1.96\sqrt{\frac{0.2714(0.7286)}{479}} = 0.3112](https://tex.z-dn.net/?f=%5Cpi%20%2B%20z%5Csqrt%7B%5Cfrac%7B%5Cpi%281-%5Cpi%29%7D%7Bn%7D%7D%20%3D%200.2714%20%2B%201.96%5Csqrt%7B%5Cfrac%7B0.2714%280.7286%29%7D%7B479%7D%7D%20%3D%200.3112)
The 95% confidence interval is (0.2316, 0.3112).
More can be learned about the z-distribution at brainly.com/question/25890103
X=1, y=-2--------------------------
Answer:
First type of fruit drinks: 48 pints
Second type of fruit drinks: 32 pints
Step-by-step explanation:
Let's call A the amount of first type of fruit drinks. 55% pure fruit juice
Let's call B the amount of second type of fruit drinks. 80% pure fruit juice
The resulting mixture should have 65% pure fruit juice and 80 pints.
Then we know that the total amount of mixture will be:
![A + B = 80](https://tex.z-dn.net/?f=A%20%2B%20B%20%3D%2080)
Then the total amount of pure fruit juice in the mixture will be:
![0.55A + 0.8B = 0.65 * 80](https://tex.z-dn.net/?f=0.55A%20%2B%200.8B%20%3D%200.65%20%2A%2080)
![0.55A + 0.8B = 52](https://tex.z-dn.net/?f=0.55A%20%2B%200.8B%20%3D%2052)
Then we have two equations and two unknowns so we solve the system of equations. Multiply the first equation by -0.8 and add it to the second equation:
![-0.8A -0.8B = -0.8*80](https://tex.z-dn.net/?f=-0.8A%20-0.8B%20%3D%20-0.8%2A80)
![-0.8A -0.8B = -64](https://tex.z-dn.net/?f=-0.8A%20-0.8B%20%3D%20-64)
![-0.8A -0.8B = -64](https://tex.z-dn.net/?f=-0.8A%20-0.8B%20%3D%20-64)
+
![0.55A + 0.8B = 52](https://tex.z-dn.net/?f=0.55A%20%2B%200.8B%20%3D%2052)
--------------------------------------
![-0.25A = -12](https://tex.z-dn.net/?f=-0.25A%20%3D%20-12)
![A = \frac{-12}{-0.25}](https://tex.z-dn.net/?f=A%20%3D%20%5Cfrac%7B-12%7D%7B-0.25%7D)
![A = 48\ pints](https://tex.z-dn.net/?f=A%20%3D%2048%5C%20pints)
We substitute the value of A into one of the two equations and solve for B.
![48 + B = 80](https://tex.z-dn.net/?f=48%20%2B%20B%20%3D%2080)
![B = 32\ pints](https://tex.z-dn.net/?f=B%20%3D%2032%5C%20pints)
Answer:
7 inches
Step-by-step explanation: Every 1 inch = 50 miles. So every 50 miles of tunnel is 1 inch in a scale drawing. 350miles/50 miles=7 inches.
The scale drawing is 7 inches.