Question

A courier service company wishes to estimate the proportion of people in various states that will use its services. Suppose the true proportion is 0.05.

If 219 are sampled, what is the probability that the sample proportion will differ from the population proportion by more than 0.03? Round your answer to four decimal places.

Answer 1

Solution:

Given:

p = the proportion of people in various states that will use courier services = 0.05

Sample Size = n = 219

We have to find:

that is:

Find standard error for proportion and divide 0.03 by standard error to get z value.

Thus we get:

Look in z table for z = 2.0 and 0.04 as well as for z = -2.0 and 0.04 and find area

P( Z< 2.04 ) = 0.9793

and

P( Z < -2.04 )= 0.0207

thus

Thus  the probability that the sample proportion will differ from the population proportion by more than 0.03 is 0.0414