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Jazlyn decided to poll town residents about making the old mill a historical site.

To obtain a confidence level of 95% (z*-score of 1.96) and an estimated margin of error of 8%, what is the approximate minimum number of randomly chosen town residents she needs to survey?

n=p(1=-p).(Z^*/E)^2

A.6 residents
B.12 residents
C.150 residents
D.600 residents

Respuesta :

aencabo
The answer is C.150 residents

Answer:

The correct option is C.

Step-by-step explanation:

From the given information it is clear that

[tex]z^*=1.96[/tex]

[tex]E=\frac{8}{100}=0.08[/tex]

The total possibilities are 2, either agree to making the old mill a historical site or disagree. The probability that the town residents will agree, is

[tex]p=\frac{1}{2}[/tex]

It is given that

[tex]n=p(1-p)\times (\frac{z^*}{E})^2[/tex]

[tex]n=\frac{1}{2}(1-\frac{1}{2})\times (\frac{1.96}{0.08})^2[/tex]

[tex]n=\frac{1}{4}\times (24.5)^2[/tex]

[tex]n=150.0625[/tex]

[tex]n\approx 150[/tex]

The minimum number of randomly chosen town residents she needs to survey is 150. Therefore option C is correct.

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