Simplify the expression 5√36^2.5

In a survey, the planning value for the population proportion is p* = 0.35. How large a sample should be taken to provide a 95%

lions [1.4K]

Answer:

$n=\frac{0.35(1-0.35)}{(\frac{0.05}{1.96})^2}=349.59$

And rounded up we have that n=350

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".

$p$ represent the real population proportion of interest

$\aht p$ represent the estimated proportion for the sample

n is the sample size required (variable of interest)

$z$ represent the critical value for the margin of error

Solution to the problem

The population proportion have the following distribution

$p \sim N(p,\sqrt{\frac{\hat p(1-\hat p)}{n}})$

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:

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

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 $ME =\pm 0.05$ 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)

And replacing into equation (b) the values from part a we got:

$n=\frac{0.35(1-0.35)}{(\frac{0.05}{1.96})^2}=349.59$

And rounded up we have that n=350

6 0

3 years ago

What percent of 4c in each expression? 0.2c

Ymorist [56]

The percentage of 4c in the expression 0.2c is 2000%

<h3>How to determine the percentage of 4c?</h3>

The expression is given as:

0.2c

The percentage of 4c is then calculated as:

4c/0.2c

Evaluate the quotient

20

Express as percentage

2000%

Hence, the percentage of 4c in 0.2c is 2000%

Read more about percentages at:

brainly.com/question/843074

#SPJ1

7 0

2 years ago

What is 4,000,000 + 700,000 + 20,000 + 9,000 + 600 + 60 + 2 in standard form?

Ivanshal [37]

Answer:

4729662

Step-by-step explanation:

5 0

3 years ago

<img src="https://tex.z-dn.net/?f=%2826%20%5Cdiv%20100%29%20%20%5C%3A%20%20%5C%3A%20%20%5C%3A%20%20%5C%3A%20%20%5Ctimes%2010" id

taurus [48]

Answer:

$\boxed{\bf \: \cfrac{13}{5}}$

Or in Decimal:

$\boxed{\bf \: 2.6}$

Step-by-step explanation:

Given expression :-

$\sf \: ( 26 \div 100) \times 10$

Solution :-

$\sf = (26 \div 100 )\times 10$

This arithmetic expression may be rewritten as ;

$\sf = \cfrac{26}{100} \times 10$

Step 1 : Cancel the zero of 10 and one zero of 100 :-

$\sf = \cfrac{26}{10 \cancel0} \times 1 \cancel0$

Results to;

$\sf = \: \cfrac{26}{10} \times 1$

$\sf = \: \cfrac{26}{10}$

Step 2: Cancel 26 and 10 by 2 :-

$\sf = \cfrac{ \cancel{26}}{ \cancel{10}}$

Results to;

$\sf = \cfrac{ \cancel{26} {}^{13} }{ \cancel{10} {}^{5} }$

$\sf = \cfrac{13}{5}$

It can also be in Decimal.

That is;

$\sf = 2.6$

Hence, the answer of the expression would be 13/5 or 2.6 .

$\rule{225pt}{2pt}$

I hope this helps!

Let me know if you have any questions.

I am joyous to help!

3 0

3 years ago

Read 2 more answers

Jenny bought 3 CDs that were each the same price. Including sales tax, she paid a total of $45.30 Of that total, $1.50 was tax.

enot [183]

Answer:

$13.6

Step-by-step explanation:

Jane bought 3 CDs that were each the same price. So let the price of each CD be ‘x’.

It is given that including sales tax, she paid a total of $45.30.

Also each CD had a tax of $1.50. We need to find out what the price of each CD was before tax.

Since the tax for all 3 CDs was same, the total amount of tax that she paid was:

3 * 1.50 = 4.50

Therefore the total tax on 3 CDs is $4.50

Since we already know the total price she paid for the CDs including taxes, we can find the price of each CD by the following way:

3x + 4.50 = 45.30

3x = 45.30 - 4.50

3x = 40.8

x = 13.6

Therefore the price of each CD before tax is $13.6.

5 0

3 years ago

Simplify the expression 5√36^2.5​

Simplify the expression 5√36^2.5