A computer system uses passwords consisting of the lowercase letters (a–z) and the integers (0–9). There are 10,000 users with unique passwords. A hacker randomly selects (with replacement) passwords in an attempt to break into the system.
(a) Suppose that 8000 of the users have six-character passwords. What is the mean and standard deviation of the number of attempts required before the hacker selects a legitimate password?
(b) Suppose that 2000 of the users have three-character passwords. What is the mean and standard deviation of the number of attempts required before the hacker selects a legitimate password?