Question

Suppose 44% of politicians are lawyers.

If a random sample of size 411 is selected, what is the probability that the proportion of politicians who are lawyers will differ from the total politicians proportion by less than 7%? Round your answer to four decimal places.

Answer 1

Solution

Given that,

p = 0.44

1 - p = 1 - 0.44 = 0.56

n = 411

= p = 0.44

=  p ( 1 - p ) / n

=   (0.44 * 0.56) / 411 = 0.0245

= 0.0245

P(0.37 < < 0.51) = P( (0.37 - 0.44) / 0.0245 < ( - ) / < (0.51 - 0.44) / 0.0245)

= P(-2.86 < z < 2.86)

= P(z < 2.86) - P(z < -2.86)

= 0.9979 - 0.0021

= 0.9958

Probability = 0.9958