HELPPPP! ABCD is a RHOMBUS. Find m

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david7962

17.09.2022

Mathematics

A sample size of at least 271 is required.

Step-by-step explanation:

We have that to find our $\alpha$ level, that is the subtraction of 1 by the confidence interval divided by 2. So:

$\alpha = \frac{1-0.9}{2} = 0.05$

Now, we have to find z in the Ztable as such z has a pvalue of $1-\alpha$ .

So it is z with a pvalue of 1-0.05 = 0.95 , so z = 1.645

Now, find the margin of error M as such

$M = z*\frac{\sigma}{\sqrt{n}}$

In which $\sigma$ is the standard deviation of the population and n is the size of the sample.

Maxium error of 0.12.

How large of a sample is required to estimate the mean usage of electricity?

We need a sample size of at least n.

n is found when $M = 0.12, \sigma = 1.2$

$M = z*\frac{\sigma}{\sqrt{n}}$

$0.12 = 1.645*\frac{1.2}{\sqrt{n}}$

$0.12\sqrt{n} = 1.645*1.2$

$\sqrt{n} = \frac{1.645*1.2}{0.12}$

$(\sqrt{n})^{2} = (\frac{1.645*1.2}{0.12})^{2}$

n = 270.6

Rounding up

A sample size of at least 271 is required.

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