7.5 A large company insists that all job applicants who are invited for interview take a psychometric test. The results of these tests follow a Normal distribution with a mean of 61 per cent and the standard deviation of 7.2 per cent.

(a) What proportion of applications would be expected to score over 70 per cent?

(b) What proportion of applications would be expected to score under 40 per cent?

(c) What proportion of applications would be expected to score between 50 per cent and 65 per cent?

(d) What score is exceeded by 20 per cent of applicants?

(e) What is the highest score achieved by the 5 per cent of applicants who do least well in the test?