Question

The population proportion is 0.60. What is the probability that a sample proportion will be within ±0.04 of the population proportion for each of the following sample sizes? Round your answers to 4 decimal places. Use z-table.

A.) n=100
B.) n= 200
C.) n=500
D.) n=1,000

Answer 1

Solution:

We are given that: The population proportion is 0.60. that is: p = 0.60

We have to find: the probability that a sample proportion will be within ±0.04 of the population proportion for each of the following sample sizes.

That is we have to find:

Part a) n = 100

Find standard Error of sample proportion:

Thus we get:

Look in z table for z = -0.8 and 0.02 as well as for z = 0.8 and 0.02

From z table we get:

P( Z < -0.82) = 0.2061

P( Z < 0.82) = 0.7939

Thus

Part b) n = 200

Find standard error

Thus we get:

Look in z table for z = -1.1 and 0.05 as well as for z = 1.1 and 0.05

From z table we get:

P( Z < -1.15) = 0.1251

P( Z < 1.15) = 0.8749

Thus

Part c) n = 500

Find standard error

Thus we get:

Look in z table for z = -1.8 and 0.03 as well as for z = 1.8 and 0.03

From z table we get:

P( Z < -1.83) = 0.0336

P( Z < 1.83) = 0.9664

Thus

Part d) n =1000

Find standard error

Thus we get:

Look in z table for z = -2.5 and 0.08 as well as for z = 2.5 and 0.08

From z table we get:

P( Z < -2.58) = 0.0049

P( Z < 2.58) = 0.9951

Thus