Helpp! how do i do this

The First National Bank of Wilson has 700 checking account customers. A recent sample of 50 of these customers showed 29 have a

attashe74 [19]

The margin of error is 0.137 and the confidence interval for the population proportion is (0.443, 0.717).

<h3>What is the margin of error(MOE)?</h3>

It is defined as an error that provides an estimate of the percentage of errors in real statistical data.

The formula for finding the MOE:

$\rm MOE = Z\times \dfrac{s}{\sqrt{n}}$

Where Z is the z-score at the confidence interval

s is the standard deviation

n is the number of samples.

We have:

n = 50, X = 29,

Estimate point p = 29/50 = 0.58

q = 1-p = 1-0.58 = 0.42

Z at 0.05/2 (95% confidence interval) = 1.96

$\rm MOE = 1.96\sqrt{\dfrac{0.58\times0.42}{50}}$

After calculating:

MOE = 0.137

Confidence interval will be: (p - MOE, p+MOE)

= (0.58-0.137, 0.58+0.137)

= (0.443, 0.717)

Thus, the margin of error is 0.137 and the confidence interval for the population proportion is (0.443, 0.717).

Learn more about the Margin of error here:

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2 years ago

What reasoning and explanations can be used when solving radical equations and how do extraneous solutions arise from radical eq

Mkey [24]

Answer:

We know that, a 'radical equation' is an equation that contains radical expressions, which further are the expressions containing radicals ( square roots and other roots of numbers ).

In order to solve radical equations, we use the rules of exponents and basic algebraic properties.

The common reasoning to use while solving a radical equation is:

1. Isolate the radical expression.

2. Square both sides of the equation to remove radical.

3. After removing the radical, solve the equation to find the unkown variable

4. Check the answer for the errors occurred by removing the radicals.

For e.g. $\sqrt{x}-3=5$

i.e. $\sqrt{x}-3+3=5+3$ ( Adding 3 on both sides )

i.e. $\sqrt{x}=8$

i.e. $(\sqrt{x})^{2} =8^{2}$

i.e. $x=64$ .

So, the solution the the radical equation $\sqrt{x}-3=5$ is x = 64.

Further, we know that an 'extraneous solution' is that root of the radical equation which is not a root of the original equation and is excluded from the domain.

for e.g. Take $\sqrt{x+4} =x-2$