An MBA graduate keeps interviewing for jobs, one by one, and will stop interviewing on receiving an offer. In each interview he has an independent probability 0.2166 of getting the job.
a. What is the expected number of interviews? What is the variance?
b. If there is enough time for only six interviews, how confident can he be of getting a job within the available time?
c. If he wants to be at least 95% confident of getting a job, how many interviews should he be prepared for?
d. Suppose there is enough time for at most six interviews. For what minimum value of p can he have 95% confidence of getting a job within the available time?
e. In order to answer (d) more thoroughly, tabulate the confidence level for p values ranging from 0.1 to 0.5 in steps of 0.05.