Question

A direct mail company wishes to estimate the proportion of people on a large mailing list that will purchase a product. Suppose the true proportion is 0.07.

If 220 are sampled, what is the probability that the sample proportion will differ from the population proportion by less than 0.04? Round your answer to four decimal places.

Answer 1

Solution

Given that,

p = 0.07

1 - p = 1 - 0.07 = 0.93

n = 220

= p = 0.07

=  p ( 1 - p ) / n

=   (0.07 * 0.93) / 220 = 0.0172

= 0.0172

P(0.03 < < 0.11) = P( (0.03 - 0.07) / 0.0172 < ( - ) / < (0.11 - 0.04) / 0.0172)

= P(2.33 < z < 2.33)

= P(z < 2.33) - P(z < -2.33)

= 0.9901 - 0.0099

= 0.9802

Probability = 0.9802