Question

Suppose 43% of the doctors in a hospital are surgeons. If a sample of 478 doctors is selected, what is the probability that the sample proportion of surgeons will be greater than 39%? Round your answer to four decimal places.

Answer 1

Solution

Given that,

p = 43% = 0.43

1 - p = 1 - 0.43 = 0.57

n = 478

= p = 0.43

=  [p( 1 - p ) / n] = [(0.43 * 0.57) / 478 ] = 0.0226

P( > 0.39 ) = 1 - P( < 0.39 )

= 1 - P(( - ) / < ( 0.39 - 0.43) / 0.0226)

= 1 - P(z < -1.77)

Using z table

= 1 - 0.0384

= 0.9616