Question

Suppose that 50% of all politicians are lawyers. If a random sample of 518 politicians is chosen, what is the probability that the proportion who are lawyers will differ from the population proportion by more than 6%

Answer 1

  

Solution

Given that,

p = 0.50

1 - p = 0.50

n = 518

= p = 0.50

=  [p ( 1 - p ) / n] = [(0.50 * 0.50) / 518] = 0.02197

= 1 - P[-0.06 / 0.02197< ( - ) / < 0.06 / 0.02197]

= 1 - P(-2.73 < z < 2.73)

= 1 - P(z < 2.73) - P(z < -2.73)

= 0.0063