In a survey 600 mothers and fathers were asked about the imp

In a survey, 600 mothers and fathers were asked about the importance of sports for boys and girls. Of the parents interviewed, 70% said the genders are equal and should have equal opportunities to participate in sports.

1. find the probability of getting at least 67% but no more than 73%. Use the exact binomial calculation.

Solution

The probability is

P(0.67<phat<0.73)

= P((0.67-0.7)/sqrt(0.7*0.3/600) <(phat-p)/sqrt(p*(1-p)/n)<(0.73-0.7)/sqrt(0.7*0.3/600))

=P(-1.60<Z<1.60) = 0.8904 (from standard normal table)