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1 Skill Qualification Task 7 - Standard deviation of the probability distribution. Dive in and email if questions:

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4 Let's say you must choose between two manufacturing contracts. Once you choose one, you must tool up the factory for that contract and you cannot take the other contract.

Saudi Arabia will buy between 10 and 18 F/A 18 Fighter Jets depending on their budget and how much pressure the US government can put on them to buy jets they don't need, but will help with US unemployment. You don't know what the final contract will be.

6 Air France will buy between 6 and 9 passenger jets, but they cannot make up their minds. They guarantee the number will be between 6 and 9 and probably one of the extremes.

7 You employ lobbyists and economists who come up with the probabilities displayed in the tables below.

8 The factory has an overhead fixed cost of 28 million dollars (administration, rent, interest, and stuff that must be paid regardless of which contract you choose).

9 The fighter jets yield a profit of 2.25 million dollars each (sell for 12.25 million each and cost 10 million to manufacture)

10 The passenger jets yield a profit of 4.5 million dollars each (sell for 30 million each and cost 25.5 million to manufacture)

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12 You can employ what you know about Expected Value to come up with the following analysis:

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F/A 18 Jet Fighters for Saudi Arabia

Passenger Jets for Air France

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No. of jets

Profit per jet Profit

Probability

No. of jets Profit per jet Profit

Probability

18

10

2.25

22.5

0.05

1.125

4.5

27

0.45

12.15

19

2.25

24.75

0.05

1.2375

4.5

31.5

0.05

.575

2.25

27

0.05

1.35

4.5

36

0.05

1.8

14

2.25

29.25

0.1

4 5

18.225

31.5

2.925

10 5

0.45

2.25

0.1

15

2.25

33.75

3.15

13.5

16

2.25

36

0.4

0.1

3.6

17

2.25

38.25

0.1

3.82

18

2.25

40 5

0.05

2.025

32.7375 Expected Value

33.75 Expected Value

28 fixed costs of the factory

28 fixed costs of the factory

4.7375 final bottom line expected net income

5.75 final bottom line expected net income

So! It looks like selling the Passenger Jets to Air France is the better idea, as it has the higher expected value.

5 But let's consider the impact of the standard deviation of the probability distribution:

The standard deviation of the probability distribution is determined by

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8 1) Subtracting the mean (expected value) from each outcome.

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2) Then square each deviation.

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3) Then multiply each squared deviation by the probability of its occurrence

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43 4) Add up the results to get the variance

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45 5) Lastly, take the square root to get the standard deviation

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