Find the area of a segment formed by a chord 8" long in a circle with radius of 8"

A candidate for a US Representative seat from Indiana hires a polling firm to gauge her percentage of support among voters in he

UkoKoshka [18]

Answer:

a) The minimum sample size is 601.

b) The minimum sample size is 2401.

Step-by-step explanation:

In a sample with a number n of people surveyed with a probability of a success of $\pi$ , and a confidence level of $1-\alpha$ , we have the following confidence interval of proportions.

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

In which

z is the zscore that has a pvalue of $1 - \frac{\alpha}{2}$ .

The margin of error is:

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

For this problem, we have that:

We dont know the true proportion, so we use $\pi = 0.5$ , which is when we are are going to need the largest sample size.

95% confidence level

So $\alpha = 0.05$ , z is the value of Z that has a pvalue of $1 - \frac{0.05}{2} = 0.975$ , so $Z = 1.96$ .

a. If a 95% confidence interval with a margin of error of no more than 0.04 is desired, give a close estimate of the minimum sample size that will guarantee that the desired margin of error is achieved. (Remember to round up any result, if necessary.)

This is n for which M = 0.04. So

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

$0.04 = 1.96\sqrt{\frac{0.5*0.5}{n}}$

$0.04\sqrt{n} = 1.96*0.5$

$\sqrt{n} = \frac{1.96*0.5}{0.04}$

$(\sqrt{n})^2 = (\frac{1.96*0.5}{0.04})^2$

$n = 600.25$

Rounding up

The minimum sample size is 601.

b. If a 95% confidence interval with a margin of error of no more than 0.02 is desired, give a close estimate of the minimum sample size necessary to achieve the desired margin of error.

Now we want n for which M = 0.02. So

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

$0.02 = 1.96\sqrt{\frac{0.5*0.5}{n}}$

$0.02\sqrt{n} = 1.96*0.5$

$\sqrt{n} = \frac{1.96*0.5}{0.02}$

$(\sqrt{n})^2 = (\frac{1.96*0.5}{0.02})^2$

$n = 2401$

The minimum sample size is 2401.

4 0

3 years ago

An excavating company charges $300 an hour for the use of a backhoe and $500 an hour for the use of a bulldozer. (part of an hou

Fed [463]

We have that

Cost use of a backhoe----------------------$300 an hour

Estimate for equipment rental each week---------------------$18,400

Total hours operator per week--------------------------------------40

40*300=$12000---------------------it is the cost per week to use a backhoe

$12000<$18400 is ok

The maximum of hours that I can rent a backhoe are 40 hours, since it is the limit of the operator and it do not overcome the total budget

4 0

3 years ago

A hardware dealer has 168kg of nails, if one nail weighs 0.25kg, how many nails he have?

snow_tiger [21]

Answer:

He has 672 nails

Step-by-step explanation:

168/.25

7 0

2 years ago

Read 2 more answers

B - (- 7) =-1 what is b?

irina1246 [14]

B-(-7)= -1

First negative multiply by negative is POSITIVE.

So: B+7= -1

Subtract 7 from both sides

B= -7-1

B= -8.

Answer: -8.

To Check Answer: Plug in the variable of B in the original equation.

So: -8-(-7)= -1

-8+7= -1

-1= -1

If the Solution works out the answer is right.

4 0

3 years ago

Read 2 more answers

The diameter of a circle is 10 cm what is the angle measure of an arc Pi centimeters long

vredina [299]

We know that

[length of a circumference]=2*pi*r
diameter=10 cm
r=10/2-----> 5 cm
[length of a circumference]=2*pi*5-----> 10*pi cm

if 360° (full circle) has a length of -----------> 10*pi cm
X°---------------------------> pi cm
X=pi*360/10*pi------> 36°

the answer is 36°

8 0

3 years ago