A recruiter for a government agency wants his candidates to be successful on a test

administered by the agency to prospective employees. He would like his group of thirty

recruits to score at least 700 out of the possible 950. Over the time this test has been

administered, the average score has been 670, with a standard deviation of 105.

(i) Estimate the probability that all thirty of the recruits will score in the 700 750 range.

(ii) Estimate the probability that all will score at least 670.

(iii) The recruiter gets a bonus if seven of the candidates score 800 or higher. Should the

recruiter look forward to a bonus?