A graduating student keeps applying for jobs until she has three offers. The probability of getting an offer at any trial is 0.48.

a. What is the expected number of applications? What is the variance?

b. If she has enough time to complete only six applications, how confident can she be of getting three offers within the available time?

c. If she wants to be at least 95% confident of getting three offers, how many applications should she prepare?

d. Suppose she has time for at most six applications. For what minimum value of p can she still have 95% confidence of getting three offers within the available time?