7 earn 5 coins

Using the z-distribution, as we are working with a proportion, it is found that the 99% confidence interval for the proportion of all U. S. Adults who would include the 9/11 attacks on their list of 10 historic events is (0.7458, 0.7942). It means that we are 99% sure that the true proportion for all U.S. adults is between these two bounds.

<h3>What is a confidence interval of proportions?</h3>

A confidence interval of proportions is given by:

$\pi \pm z\sqrt{\frac{\pi(1-\pi)}{n}}$

In which:

$\pi$ is the sample proportion.

z is the critical value.

n is the sample size.

In this problem, the parameters are:

$z = 2.575, n = 2000, \pi = 0.77$

The lower limit of this interval is:

$\pi - z\sqrt{\frac{\pi(1-\pi)}{n}} = 0.77 - 2.575\sqrt{\frac{0.77(0.23)}{2000}} = 0.7458$

The upper limit of this interval is:

$\pi + z\sqrt{\frac{\pi(1-\pi)}{n}} = 0.77 + 2.575\sqrt{\frac{0.77(0.23)}{2000}} = 0.7942$

The 99% confidence interval for the proportion of all U. S. Adults who would include the 9/11 attacks on their list of 10 historic events is (0.7458, 0.7942). It means that we are 99% sure that the true proportion for all U.S. adults is between these two bounds.

More can be learned about the z-distribution at brainly.com/question/25890103

7 0

2 years ago

A party rental company has chairs and tables for rent. The total cost to rent 3 chairs and 2 tables is $18. The total cost to re

DerKrebs [107]

C= chair cost
t= table cost

Create two equations with the given information. Solve for one variable in equation one. Substitute that answer in equation two. Then you can solve for the needed information.
3c+2t=$18
5c+6t=$48

3c+2t=18
Subtract 2c from both sides
3c=18-2t
Divide both sides by 3
c=(18-2t)/3

Substitute the value for c in equation two:
5c+6t=$48
5((18-2t)/3)+6t=48
(90-10t)/3+6t=48
Multiply everything by 3 to eliminate fraction
(3)((90-10t)/3)+(3)(6t)=(3)(48)
90-10t+18t=144
90+8t=144
Subtract 90 from both sides
8t=54
Divide both sides by 8
t=$6.75 cost for table

Substitute the t value to solve for c:
3c+2t=18
3c+2(6.75)=18
3c+13.50=18
3c=4.50
c=$1.50 chair cost

Check:
5c+6t=$48
5(1.50)+6(6.75)=48
7.50+40.50=48
48=48

Hope this helps! :) If it does, please mark as brainliest.

7 0

2 years ago