Please show me the step by step solution hand method that the question asks for,
ID: 3257564 • Letter: P
Question
Please show me the step by step solution hand method that the question asks for, I need to understand how to solve these, thanks!
Probability Problem
An electric utility is experiencing a difficult time obtaining natural gas for electric generation. Fuels other than natural gas (called fuel-mixes) are purchased at an extra cost, which is transferred to the customer. Total monthly fuel expenses are now averaging $7,750,000.
An engineer with the city-owned utility has calculated the average revenue for the past 24 months using three fuel-mix situations –
Gas Plentiful
< 30% other fuels purchased
>=30% other fuels purchased
The table below indicates the number of months that each fuel-mix situation occurred (i.e Gas Plentiful occurred 12 out of the last 24 months).
Can the utility expect to meet future monthly expenses based on the 24 months of data, if a similar fuel-mix pattern continues? (i.e. what is the expected EMV?) You can use Excel or do this by hand (5 points)
Revenue & Fuel Mix Data
Fuel-Mix Situation
Months in Past 24
Average Revenue,
$ per Month
Gas plentiful
12
5,270,000
<30% other
6
7,850,000
>= 30% other
6
12,130,000
Revenue & Fuel Mix Data
Fuel-Mix Situation
Months in Past 24
Average Revenue,
$ per Month
Gas plentiful
12
5,270,000
<30% other
6
7,850,000
>= 30% other
6
12,130,000
Explanation / Answer
Solution
Concept Base
1. Gas Plentiful occurred 12 out of the last 24 months
=> P(Gas Plentiful) = 12/24 = 0.5.
Similarly, P(<30% other) = 6/24 = 0.25 and P(>=30% other) = 6/24 = 0.25.
2. EMV = [over x]{x.P(x)}, where x = value and P(x) is the corresponding probability.
3. The utility is expected to meet future monthly expenses if EMV of per month
revenue > 7,750,000 (i.e., Total monthly fuel expenses on an average).
Now, to work out the problem,
Fuel-Mix Situation
Probability P(x)
Average Revenue
EMV = x.P(x)
$ per Month (x)
Gas plentiful
0.5
5,270,000
2635000
<30% other
0.25
7,850,000
1962500
>= 30% other
0.25
12,130,000
3032500
TOTAL
7630000
Conclusion: Since 7630000 < 7,750,000, the utility is not expected to meet
total monthly fuel expenses on an average.
DONE
Fuel-Mix Situation
Probability P(x)
Average Revenue
EMV = x.P(x)
$ per Month (x)
Gas plentiful
0.5
5,270,000
2635000
<30% other
0.25
7,850,000
1962500
>= 30% other
0.25
12,130,000
3032500
TOTAL
7630000
Related Questions
drjack9650@gmail.com
Navigate
Integrity-first tutoring: explanations and feedback only — we do not complete graded work. Learn more.