Question

Suppose 52% of the doctors in a hospital are surgeons. If a sample of 563 doctors is selected, what is the probability that the sample proportion of surgeons will differ from the population proportion by less than 5%? Round your answer to four decimal places

Answer 1

Solution

Given that,

=  [p ( 1 - p ) / n] =   [(0.52 * 0.48) / 563 ] = 0.0211

= P[(-0.05) /0.0211 < ( - ) / < (0.05) / 0.0211]

= P(-2.37 < z < 2.37)

= P(z < 2.37) - P(z < -2.37)

= 0.9911 - 0.0089

= 0.9822

Probability = 0.9822