One day you may find yourself detailed to a recruiting district as Operations Officer. (Lucky you, that's shore duty!) But you will quickly find out that "making quota" is critical to your success. In other words, "heads will roll" if your recruiters don't reach the set goals for the number of recruits signed on each month. (You could find yourself back at sea with less than stellar fitreps.)

It is getting close to the end of the month and your office still needs 5 recruits to "make quota".

1. If there is a 40% chance that someone who is interviewed will become a recruit,

a. What is the probability that the recruiters will have to interview more than 10 people to "make quota"?

b. With 90% certainty, what is the largest number of people that must be interviewed to "make quota"?

2. If 1 out of 5 recruits belong to a racial minority group and you have signed on 35 recruits by the end of the month, what is the probability that more than 6 are minority recruits?

3. You decide that you better make a road trip to some high schools in your area to see if you can get the recruits that you need. In your region, high schools are pretty spread out, about 1 every 10 miles.

a. What is the probability that you will come to a high school within 8 miles?

b. What is the probability that you will have to drive more than 50 miles to find 6 high schools?

4. When you get to one of the high schools, all the students that are interested in joining the Navy have been assembled in the cafeteria. However, 15 of the students are seriously interested in hearing about what the Navy has to offer, the other 10 just wanted to get out of class. Since you only want to talk to the serious students, you randomly pick 20 students,

a. What is the probability that you got all the students that are genuinely interested?

b. What is the probability that you got at least 12 of those that are interested and at least 3 of the others?

5. You know that you will only sign up 1 recruit out of 4 high school visits. What is the chance that you will "make quota" within 300 miles? (HINT: Watch your units!)

6. You normally talk to an average group of 20 students at each high school presentation. If you stop at 10 high schools, what is the probability of stopping at no more than 4 high schools with groups of at least 25 students?

7. Match the description with its appropriate distribution(s).

I. Binomial

II. Negative Binomial

III. Hypergeometric

IV. Poisson

V. Exponential

VI. Erlang

A. P = prob(success) is one of the parameters

B. N = # of trials is one of the parameters

C. The random variable is time to complete the next event

D. X = # of successes

E. Probability problems are solved by conversion to a binomial distribution

F. Has continuous random variables

G. Is memory less