In a multiple choice test, each question has four answers, A, B, C and D, only one of which is correct. The total number of questions is 20. Students need to obtain at least 6 correct answers to pass the test and all of them guess the answers.

(i) the probability that a randomly selected student passes the test ?

(ii) if 100 students sit for the test, use the normal approximation to the binomial distribution to find the probability that more than 50 students pass the test. answer in 4 decimal places.

(iii) An employment company wants to estimate the proportion of fresh graduates

who are still unemployed after one year of graduation in Canada. A random sample of 400 fresh graduates is taken and it is found that 124 are unemployed. Construct an approximate 95% confidence interval for the true proportion of

fresh graduates who are still unemployed after one year of graduation. answer to 3 decimal places.