Question

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 1

Answer:

0.000024

Step-by-step explanation:

n = 628

42% of politicians are lawyers

So , Population proportion , $\widehat{p}=0.42$

Sample proportion p= 0.5

We are supposed to find$P(\widehat{p}$

Formula : $z=\frac{p-\widehat{p}}{\frac{\widehat{p}(1-\widehat{p})}{n}}$

Substitute the values :

$z=\frac{0.5-0.42}{\sqrt{\frac{0.42(1-0.42)}{628}}}$

$z=4.061$

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