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Forecasting, Exponential Smoothing, Seasonal Index

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Question (1)
A food distributor carries 64 varieties of salad dressing. Appleton Markets stocks 48 of these flavors. Beacon Stores carries 32 of them. The probability that a flavor will be carried by Appleton or Beacon is 15/16. Find the probability a flavor is carried by both Appleton and Beacon.

Question (2)
The time it takes to travel from home to the office is normally distributed with  = 25 minutes and  = 5 minutes.

a. What is the probability the trip takes more than 20 minutes?
b. What is the probability the trip takes less than 15 minutes?
c. What is the probability the trip takes between 30 and 35 minutes?
d. What is the probability the trip takes more than 40 minutes?

Question (3)
The table shows both prospective profits and losses for a company, depending on what decision is made and what state of nature occurs. Use the information to determine what the company should do. (please see the attachment for the pay off table and the full description of the question)
(a) if an optimistic strategy is used.
(b) if a conservative strategy is used.
(c) if minimax regret is the strategy.
Question (4)
Dollar Department Stores has the opportunity of acquiring either 3, 5, or 10 leases from the bankrupt Granite Variety Store chain. Dollar estimates the profit potential of the leases depends on the state of the economy over the next five years. There are four possible states of the economy as modeled by Dollar Department Stores, and its president estimates P(s1) = .4, P(s2) = .3, P(s3) = .1, and P(s4) = .2. The utility has also been estimated. Given the payoffs (in $1,000,000's) and utility values below, which decision should Dollar make using expected utility as its decision criterion?( Please see the attachment for full description of question)
Question (5)
The number of girls who attend a summer basketball camp has been recorded for the seven years the camp has been offered. Use exponential smoothing with a smoothing constant of .8 to forecast attendance for the eighth year.

47, 68, 65, 92, 98, 121, 146
Question (6)
Monthly sales at a coffee shop have been analyzed. The seasonal index values are
( please see the attachment for full description of question )
and the trend line is 74123 + 26.9(t).

Assuming there is no cyclical component - but that there is a seasonal component -- forecast sales for year 8 (months 97 - 108).

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Solution Summary

Six problems given in the Problems section of this page are solved with step by step explanation and the required graphs and tables. The problems are from Normal Probabilit Distribution, Time Series Analysis, Decision Analysis and other topics. The solutions are given in easy to understand language , notations and format so that the student could solve other problems of the same type independently with the help of these solutions.
Solutions to problems on Decision Theory, Forecasting involved the use of Exponential smoothing and Seasonal Index, and deseasonlization are given with step by step explanation so that the students could easily understand the method and use these solutions to solve other similar problems using these solutions as model solutions. Problems on using optimistic strategy, conservative strategy, minimax regret in decision analysis are explained in simple language and are given in minute detail. Besides this, problems on Probability, and Normal distribution are also given with step by step explanation and all the working. For all this, please download the attached solution file.

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Solution (1)
Probability that a flavor is available with Appleton = P(A) = 3/4
Therefore, the probability that a flavor is available with both = = 5/16=0.3125
(For step by step solution of the question, please see the attached file )

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