Question

Suppose 55% of the doctors in America are dentists. If a random sample of size 405 is selected, what is the probability that the proportion of doctors who are dentists will differ from the population proportion by less than 6%? Round your answer to four decimal places.

Answer 1

Solution

Given that,

p = 0.55

1 - p = 1 - 0.55 = 0.45

n = 405

= p = 0.55

=  p ( 1 - p ) / n

=   (0.55 * 0.45) / 405 = 0.02472

= 0.02472

P(0.49 < < 0.61) = P( (0.49 - 0.55) / 0.02472 < ( - ) / < (0.61 - 0.55) / 0.02472)

= P(-2.43 < z < 2.43)

= P(z < 2.43) - P(z < -2.43)

= 0.9925 - 0.0075

= 0.985

Proportion = 0.9850