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xenn [34]
3 years ago
14

Rearrange the formula S = a/(a - r) for r.

Mathematics
2 answers:
vesna_86 [32]3 years ago
7 0
S = a / (a - r)...multiply both sides by (a - r)
S(a - r) = a
Sa - Sr = a
Sa - a = Sr
(Sa - a) / S = r or it could be : (aS - a) / S = r
scZoUnD [109]3 years ago
3 0
S = a/(a - r)
s(a - r) = a
sa - sr = a
sr = sa - a
sr = a(s - 1)
r = (a(s - 1))/s
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Ilia_Sergeevich [38]

Using the z-distribution, a sample of 142,282 should be taken, which is not practical as it is too large of a sample.

<h3>What is a z-distribution confidence interval?</h3>

The confidence interval is:

\overline{x} \pm z\frac{\sigma}{\sqrt{n}}

The margin of error is:

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

In which:

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Assuming an uniform distribution, the standard deviation is given by:

S = \sqrt{\frac{(4 - 0)^2}{12}} = 1.1547

In this problem, we have a 95% confidence level, hence\alpha = 0.95, z is the value of Z that has a p-value of \frac{1+0.95}{2} = 0.975, so the critical value is z = 1.96.

The sample size is found solving for n when the margin of error is of M = 0.006, hence:

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

0.006 = 1.96\frac{1.1547}{\sqrt{n}}

0.006\sqrt{n} = 1.96 \times 1.1547

\sqrt{n} = \frac{1.96 \times 1.1547}{0.006}

(\sqrt{n})^2 = \left(\frac{1.96 \times 1.1547}{0.006}\right)^2

n =  142,282.

A sample of 142,282 should be taken, which is not practical as it is too large of a sample.

More can be learned about the z-distribution at brainly.com/question/25890103

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Two events A and B are said to be independent, if P(A∩B) = P(A) P(B)

We have, P(A|B) = P(A∩B)/P(B)

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Now P(A) P(B) = 0.5 x 0.8 = 0.4

So P(A∩B) ≠ P(A)P(B)

Therefore, the events A and B are not independent.

Learn more about independent events at brainly.com/question/22881926

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Step-by-step explanation:

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