Question

The population proportion is 0.40. 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.) (a) n = 100

Answer 1

Solution :

Given that ,

p = 0.40

1 - p = 0.60

a)

n = 100

= p = 0.40  

= (p*(1-p))/n =  (0.40*0.60)/ 100= 0.04899

P(0.36 < <0.44 ) = P((0.36-0.40)/0.04899 ) < ( - ) /  < (0.44-0.40) /0.04899 ) )

= P(-0.82 < z < 0.82)

= P(z < 0.82) - P(z < -0.82)

= 0.7939 - 0.2061

= 0.5878

Probability = 0.5878