Solve for r 12-1/5r=2r+1

Nitrates are groundwater contaminants derived from fertilizer, septic tank seepage and other sewage. Nitrate poisoning is partic

o-na [289]

Answer:

a) $n=\frac{0.5(1-0.5)}{(\frac{0.02}{1.96})^2}=2401$

And rounded up we have that n=2401

b) $n=\frac{0.07(1-0.07)}{(\frac{0.02}{1.96})^2}=625.22$

And rounded up we have that n=626

And we see that if we have previous info about p the sample size varies a lot.

Step-by-step explanation:

Previous concepts

A confidence interval is "a range of values that’s likely to include a population value with a certain degree of confidence. It is often expressed a % whereby a population means lies between an upper and lower interval".

The margin of error is the range of values below and above the sample statistic in a confidence interval.

Normal distribution, is a "probability distribution that is symmetric about the mean, showing that data near the mean are more frequent in occurrence than data far from the mean".

Solution to the problem

In order to find the critical value we need to take in count that we are finding the interval for a proportion, so on this case we need to use the z distribution. Since our interval is at 95% of confidence, our significance level would be given by $\alpha=1-0.95=0.05$ and $\alpha/2 =0.025$ . And the critical value would be given by:

$z_{\alpha/2}=-1.96, z_{1-\alpha/2}=1.96$

Part a

The margin of error for the proportion interval is given by this formula:

$ME=z_{\alpha/2}\sqrt{\frac{\hat p (1-\hat p)}{n}}$ (a)

And on this case we have that $ME =\pm 0.02$ and we are interested in order to find the value of n, if we solve n from equation (a) we got:

$n=\frac{\hat p (1-\hat p)}{(\frac{ME}{z})^2}$ (b)

Since we don't have prior information about the population proportion we can use ase estimator $\hat p =0.5$ . And replacing into equation (b) the values from part a we got:

$n=\frac{0.5(1-0.5)}{(\frac{0.02}{1.96})^2}=2401$

And rounded up we have that n=2401

Part b

For thi case the estimator for p is $\hat p =0.07$

$n=\frac{0.07(1-0.07)}{(\frac{0.02}{1.96})^2}=625.22$

And rounded up we have that n=626

And we see that if we have previous info about p the sample size varies a lot.

4 0

3 years ago

What is the value of x<br><br> Triangle with sides 10 6 x-6

Grace [21]

Given that the triangle is a right angled triangle, to solve for x we shall use the Pythagorean theorem given by:
c^2=a^2+b^2
where:
c is the hypotenuse
a and b are the legs.
c=10
a=6
b=(x-6)
thus plugging the values in the equation and solving for x we get:
10^2=6^2+(x-6)^2
100=36+x^2-12x+36
100=x^2-12x+72
0=x^2-12x-28
factoring the above we get:
0=(x+2)(x-14)
hence
x=-2 or x=14
given that there is no negative distance then
x=14
thus the value of x is 14

5 0

3 years ago

Jane needs to pay $36 for 2 basketballs, how much she needs to pay 3 basketballs?

OLga [1]

36 divided by 2 is 18

That mean each basketball is $18

18 dollars multiplied by 3 basketballs is 54

Three basket balls cost $54

5 0

3 years ago

Read 2 more answers

An abstract sculpture in the form of a triangle has a base 21 meters and a height of 12 meters. Find the are of the triangle.

charle [14.2K]

The area of a triangle could be determined using the following formula
$\boxed{a= \frac{1}{2} \times b \times h}$

plug in the numbers
$a = \frac{1}{2} \times 21 \times 12$
$a = \frac{1}{2} \times 252$
$a= \frac{252}{2}$
a = 126

The area of the triangle is 126 square meters

8 0

3 years ago

It is about solving equations by substitution. if you can help plzzz

Lyrx [107]

Message me, and i can help more:)

6 0

3 years ago