In the following situations identify the appropriate probability
distribution. Give its parameters. Use the user-defined functions
of the Random Variables Add-in to answer
the numerical questions.
a. A department at the University has twenty professors. Ten
are full professors, four are associate professors and six are
assistant professors. The chairman selects four names at random
from the faculty to form a committee. What is the probability
at least three members of the committee are full professors?
b. You have the job of hiring three workers to accomplish some
task. Twenty candidates are waiting for interviews. You will
interview each candidate in turn, and if he or she is acceptable
you will hire the person immediately. The probability that a
candidate is acceptable is 0.6. What is the probability that
you will fill the three positions with ten or fewer interviews?
c. A major company needs three engineers but will accept more.
The manager in charge of hiring will conduct ten interviews
in hopes of finding at least three good applicants
who will accept the offer of a job. The probability that an
applicant is good is 0.4, and the probability that
a good applicant will accept the job is 0.6. She
makes offers to every good applicant. We assume
applicants are independent. What distribution describes the
number of engineers she will hire? What is the probability that
at least three will be hired?
d. A robot insertion tool must place 4 rivets on a printed
circuit board. Rivets are presented to it at random, but 10%
of the rivets are faulty. When a faulty rivet is encountered
it must be discarded, and another drawn. We want to compute
probabilities regarding the number of draws required before
4 good rivets are found. In particular what is the probability
that exactly 10 draws are required before we find 4 good rivets.