A survey conducted by Certified Practising Accountants Australia to investigate the reaction to new audit standards issued by the Auditing and Assurance Standards Board finds that only 53% of Australian auditors believe the new standards have improved audit quality. Fifty-eight per cent of auditors feel the standards have improved confidence in financial reporting. Assume that these two events (improved quality and improved confidence) are independent. Suppose 20 auditors from Australia are selected at random.

(a) What is the probability that fewer than 15 of them believe the standards have improved confidence in financial reporting?

(b) What is the expected number of auditors who believe the standards have improved confidence in financial reporting?

(c) What is the probability that more than 10 of them believe the new standards have improved audit quality?

(d) On average, how many of them feel the new standards have improved audit quality?

(e) What is the probability that exactly 10 of them believe the new standards have improved both confidence in financial reporting and audit quality?

(f) What is the probability that at least 10 of them believe the new standards have improved both confidence in financial reporting and audit quality?

(g) What is the expected number of auditors who believe the new standards have improved both confidence in financial reporting and audit quality?