Question

Suppose 59% of politicians are lawyers.

If a random sample of size 750 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

olution

Given that,

p = 0.59

1 - p = 1 - 0.59 = 0.41

n = 750

= p = 0.59

=  p ( 1 - p ) / n

=   (0.59 * 0.41) / 750 = 0.01796

P(0.54 < < 0.64) = P( (0.54 - 0.59) / 0.01796 < ( - ) / < (0.64 - 0.59) / 0.01796)

= P(-2.784 < z < 2.784)

= P(z < 2.784) - P(z < -2.784)

= 0.9973 - 0.0027

= 0.9946

Probability = 0.9946