Question

Suppose 50% of the population has a college degree. If a random sample of size 673 is selected, what is the probability that the proportion of persons with a college degree will differ from the population proportion by less than 5%? Round your answer to four decimal places.

Answer 1

Sample size, n = 673

Population proportion, P = 0.50

The probability that the proportion of persons with a college degree will differ from the population proportion by less than 5%,  $P(-0.05<\bar p-P < 0.05)$ =

$=P\left [ \frac{-0.05}{\sqrt{0.50(1-0.50)/673}}<\frac{\bar p-P}{\sqrt{P(1-P)/{n}}}<\frac{0.05}{\sqrt{0.50(1-0.50)/673}} \right ]$

$=P\left [ -2.594<Z<2.594\right ]$

$=P[ Z<2.594]-P[Z<-2.594]$

From standard normal table

$=0.9953-0.0047 = \textbf{0.9906}$