Question

A population proportion is 0.3. A sample of size 250 will be taken and the sample proportion p^- will be used to estimate the population proportion. Use z-table. Round your answers to four decimal places. Do not round intermediate calculations.

a. What is the probability that the sample proportion will be within plus or minus 0.03 of the population proportion?

b. What is the probability that the sample proportion will be within plus or minus 0.06 of the population proportion?

Answer 1

Solution:

Given:

p = Population proportion = 0.3

n = Sample Size = 250

Part a) We have to find the probability that the sample proportion will be within plus or minus 0.03 of the population proportion.

That is:

Divide each term inside probability equation by standard deviation of sample proportion.

That is by:

Thus

Look in z table for z = 1.0 and 0.04 as well as for  z = -1.0 and 0.04  and find corresponding area.

P( Z<1.04) = 0.8508

and

P( Z< -1.04) = 0.1492

Thus

Part b) Find  the probability that the sample proportion will be within plus or minus 0.06 of the population proportion.

That is:

Thus

Look in z table for z = 2.0 and 0.07 as well as for  z = -2.0 and 0.07  and find corresponding area.

P( Z< 2.07) = 0.9808

and

P( Z< -2.07) =0.0192

Thus