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Suppose 42% of politicians are lawyers. If a random sample of size 628 is selected, what is the probability that the proportion of politicians who are lawyers will differ from the total politicians proportion by less than 5%? Round your answer to four decimal places.

Answer :

Answer:

0.000024

Step-by-step explanation:

n = 628

42% of politicians are lawyers

So , Population proportion , [tex]\widehat{p}=0.42[/tex]

Sample proportion p= 0.5

We are supposed to find[tex]P(\widehat{p}<0.5)[/tex]

Formula : [tex]z=\frac{p-\widehat{p}}{\frac{\widehat{p}(1-\widehat{p})}{n}}[/tex]

Substitute the values :

[tex]z=\frac{0.5-0.42}{\sqrt{\frac{0.42(1-0.42)}{628}}}[/tex]

[tex]z=4.061[/tex]

p value = 0.000024

So,the probability that the proportion of politicians who are lawyers will differ from the total politicians proportion by less than 5% is 0.000024

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