Question

Suppose that 60% of student voters support a candidate for students' council president. Find the probability that a sample of 1,000 student voters would yield a sample proportion in favor of the candidate within 4 % points of the actual proportion

Answer 1

Solution :

Given that ,

p = 0.60

1 - p = 0.40

n = 1000

= p = 0.60  

= (p*(1-p))/n =  (0.60*0.40)/ 1000= 0.01549

P(0.56< < 0.64 ) = P((0.56-0.60)/0.01549 ) < ( - ) /  < (0.64-0.60) /0.01549 ) )

= P(-2.58 < z < 2.58 )

= P(z < 2.58) - P(z < -2.58)

= 0.9951 - 0.0049

= 0.9902

Probability = 0.9902