Probability Distribution – Computing mean and variance

Question description

Unless otherwise stated, answer in
complete sentences, and be sure to use correct English spelling and
grammar.  Sources must be cited in APA
format.  Your response should be a
minimum of one (1) single-spaced page to a maximum of two (2) pages
in length; refer to the “Assignment Format” page for specific
format requirements.

NOTE:
Show your work in the problems.
1.  Compute the mean and variance of the
following discrete probability distribution.
 

x

P(x)

2

.50

8

.30

10

.20

 
2.  The Computer Systems Department has eight
faculty, six of whom are tenured.  Dr.
Vonder, the chair, wants to establish a committee of three department faculty
members to review the curriculum.  If she
selects the committee at random:
    a.  What is the probability all members of the
committee are tenured?
b.  What is the probability that at least one
member is not tenured?  (Hint:  For this question, use the complement rule.)
3.  New Process, Inc., a large mail-order
supplier of women’s fashions, advertises same-day service on every order.  Recently, the movement of orders has not gone
as planned, and there were a large number of complaints.  Bud Owens, director of customer service, has
completely redone the method of order handling. 
The goal is to have fewer than five unfilled orders on hand at the end
of 95% of the working days.  Frequent
checks of the unfilled orders follow a Poisson distribution with a mean of two
orders.  Has New Process, Inc. lived up
to its internal goal?  Cite evidence.
4.  Recent information published by the U.S.
Environmental Protection Agency indicates that Honda is the manufacturer of
four of the top nine vehicles in terms of fuel economy.
  a.  Determine
the probability distribution for the number of Hondas in a sample of three cars
chosen from the top nine.
b.  What is the likelihood that in the sample of
three at least one Honda is included?
5.  According to the “January theory,” if the
stock market is up for the month of January, it will be up for the year.  If it is down in January, it will be down for
the year.  According to an article in the
Wall Street Journal, this theory held
for 29 out of the last 34 years.  Suppose
there is no truth to this theory.  What
is the probability this could occur by chance?