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 more than 5%? Round your answer to four decimal places.

Answer 1

n = 563

p = 0.52

= p = 0.52

= sqrt(p(1 - p)/n)

= sqrt(0.52(1 - 0.52)/563)

= 0.0211

P(0.47 < < 0.57)

= P((0.47 - )/ < ( - )/ < (0.57 - )/)

= P((0.47 - 0.52)/0.0211 < Z < (0.57 - 0.52)/0.0211)

= P(-2.37 < Z < 2.37)

= P(Z < 2.37) - P(Z < -2.37)

= 0.9911 - 0.0089

= 0.9822