An interval estimate is an interval calculated from the population data, where we
strongly believe the true value of the population parameter lies.
We compute the five-period moving averages for all time periods except the first two.
The binomial distribution can be well approximated by the normal distribution when
the number of trials n is sufficiently small and the probability of success p is not too
close to 0 or 1.
A forward procedure is a type of equation building procedure that begins with only one
explanatory variable in the regression equation and successively adds one variable at a
time until no remaining variables make a significant contribution.
What is the probability that no one is waiting or being served in the express checkout
line?
The Poisson distribution is characterized by a single parameter , which must be
positive.
NARRBEGIN: SA_79_83
Suppose that the manufacturer of a particular product assesses the joint distribution of
the price per unit (P) and demand (D) for its product in the upcoming quarter as
presented below. Use this information to answer the following questions.
Demand (D)
NARREND
What is the probability that the demand of this product will be less than 3500 units in
the upcoming quarter, given that its price will be greater than $20?
NARRBEGIN: SA_91_103
A sample of 1000 households was selected in Los Angeles to determine information
concerning consumer behavior. Among the questions asked was “Do you enjoy
shopping for clothing?” Of 480 males, 272 answered yes. Of 520 females, 448
answered yes.
NARREND
What is the probability that a respondent chosen at random is a male?
Football teams toss a coin to see who will get their choice of kicking or receiving to
begin a game. The probability that given team will win the toss three games in a row is
0.125.
As a general rule, the normal distribution is used to approximate the sampling
distribution of the sample proportion only if the sample size n is greater than 30.
On average, how many customers would you expect to see in each of these two lines at
the grocery store?
NARRBEGIN: SA_74_77
The “winner’s curse” refers to a situation where there are several bidders on the same
item. Each participant can make his or her independent estimate for the value of the
item. When all participants are equally informed their estimates will be unbiased, but,
given the difficulty of estimating the value, the estimates may vary widely. Even though
the mean of the estimates may equal the expected value, the winner’s bid will likely be
more than the value of the item. Consider a case where 3 companies are trying to decide
how much to bid for a commercial real estate tract. Assume that each bidder
independently estimates the value of the tract. This estimated value is a random variable
that for each bidder is drawn from a normal distribution with a mean of $1,000,000 and
a standard deviation of $200,000. The actual value is also drawn from the same
distribution.
NARREND
Next, assume that one of the bidders bids 20% below his or her estimated value, while
the other two bidders follow the same strategy as in Question 74. Using 1000 iterations
report the expected profit or loss to the conservative bidder.
NARRBEGIN: SA_51_56
A firm is considering investing $0.9M in a typical industrial manufacturing application
with a three year production planning cycle under a forecasted market price
environment. A simple three-period project pro forma cash flow sheet for this project is
shown below:
In the pro forma, the production and price forecast in each period translate to revenue,
which can then be netted of production costs to arrive at the expected cash flow in each
period. The cash flows are then be discounted at a rate that is commensurate with the
riskiness of the project (here, assumed to be 10%).
NARREND
What are the chances the firm could loose money on this project, given the price
uncertainty?
NARRBEGIN: SA_102_103
Suppose that a decision maker’s risk attitude toward monetary gains or losses x given by
the utility function U(x) =
NARREND Show that this decision maker is indifferent between gaining nothing and
entering a risky situation with a gain of $80,000 (probability 1/3) and a loss of $10,000
(probability 2/3).
