Probability Analysis
r-rover
analysis_demand.docxA General Manger of Harley-Davidson has to decide on the size of a new facility. The GM has narrowed the choices to two: large facility or small facility. The company has collected information on the payoffs. It now has to decide which option is the best using probability analysis, the decision tree model, and expected monetary value.
Options:
Facility Demand Probability Actions Expected
Large Low demand 0.4 Do nothing ($10)
Low Demand 0.4 Reduce prices $50
High Demand 0.6 $70
Small Low demand 0.4 $40
High Demand 0.6 Do Nothing $40
High Demand 0.6 Overtime $50
High Demand 0.6 Expand $55
Determination of chance probability and respective payoffs:
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Build Small: |
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Low Demand |
0.4($40)=$16 |
|
High Demand |
0.6($55)=$33 |
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|
|
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Build Large: |
|
|
Low Demand |
0.4($50)=$20 |
|
High Demand |
0.6($70)=$42 |
Determination of Expected Value of each alternative Build Small: $16+$33=$49 Build Large: $20+$42=$62
Click here for the Statistical Terms review sheet.
SAMPLING MEAN:
DEFINITION:
The term sampling mean is a statistical term used to describe the properties of statistical distributions. In statistical terms, the
sample mean
from a group of observations is an estimate of the population mean. Given a sample of size n, consider n independent random variables X1, X2... Xn, each corresponding to one randomly selected observation. Each of these variables has the distribution of the population, with mean
and standard deviation
. The sample mean is defined to be
WHAT IT IS USED FOR:
It is also used to measure central tendency of the numbers in a database. It can also be said that it is nothing more than a balance point between the number and the low numbers.
HOW TO CALCULATE IT:
To calculate this, just add up all the numbers, then divide by how many numbers there are. Example: what is the mean of 2, 7, and 9? Add the numbers: 2 + 7 + 9 = 18 divide by how many numbers (i.e., we added 3 numbers): 18 ÷ 3 = 6 so the Mean is 6
