Question

The population proportion is 0.65 . What is the probability that a sample proportion will be within plus or minus 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

Here' the answer to the question with full concept. Please don't hesitate to give a "thumbs up" in case you're satisfied with the answer

a. n = 100

p = .65

p-p'= .04

So, P(|p|<= .04) = P( |Z| < = .04/sqrt(.65*.35/100) = P(|Z|<=.84) = 2*P(0<Z<.84) = 2*(.799-.5) = .598

b.

So, P(|p|<= .04) = P( |Z| < = .04/sqrt(.65*.35/200) = P(|Z|<=.84) = 2*P(0<Z<1.186)

= 2*(.882-.5)

=0.7644 c. n =500

So, P(|p|<= .04) = P( |Z| < = .04/sqrt(.65*.35/500) = P(|Z|<=1.88)

=.9392

d.

So, P(|p|<= .04) = P( |Z| < = .04/sqrt(.65*.35/1000) = P(|Z|<=2.65) = 2*P(0<Z<2.65) = .9920