Question

A researcher believes that 8% of males smoke cigarettes.

If the researcher is correct, what is the probability that the proportion of smokers in a sample of 512 males would differ from the population proportion by greater than 3%? Round your answer to four decimal places.

Answer 1

Solution

Given that,

=  [p ( 1 - p ) / n] = [(0.08 * 0.92) / 512 ] = 0.0120

= 1 - P[(-0.03) /0.0120 < ( - ) / < (0.03) / 0.0120]

= 1 - P(-2.5 < z < 2.5)

= 1 - P(z < 2.5) - P(z < -2.5)

= 1 - P(0.9938 - 0.0062)

= 1 - 0.9876

= 0.0124

Probability = 0.0124