If n = 6, what is the value of 9n−4?
2 answers:
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Answer:
1) The expected value of the "winnings" is $(-0.97)
2) The variance for the "winnings" is $0.57966
3) The standard deviation for the "winnings" is$0.761354
4) The game is not a fair game because one is expected to lose $0.97
Step-by-step explanation:
1) The probability of having a sum of 2 = 1/6×1/6 = 1/36
The probability of having a sum of 3 = 1/6×1/6 = 1/36
The probability of having a sum of 4 = 1/6×1/6 + 1/6×1/6 = 1/18
The probability of having a sum of 5 = 1/6×1/6 + 1/6×1/6 = 1/18
The probability of having a sum of 6 = 1/6×1/6 + 1/6×1/6 + 1/6×1/6 = 1/12
The probability of having a sum of 7 = 1/6×1/6 + 1/6×1/6 + 1/6×1/6 = 1/12
The probability of having a sum of 8 = 1/6×1/6 + 1/6×1/6 + 1/6×1/6 = 1/12
The probability of having a sum of 9 = 1/6×1/6 + 1/6×1/6 = 1/18
The probability of having a sum of 10 = 1/6×1/6 + 1/6×1/6 = 1/18
The probability of having a sum of 11 = 1/6×1/6 = 1/36
The probability of having a sum of 12 = 1/6×1/6 = 1/36
The values are;
For 2, we have 1/36 × (20 - 5) = 0.41
For 3, we have 1/36 × (20 - 5) = 0.41
For 4, we have 1/18 × (20 - 5) = 0.8
For 5, we have 1/18 × (10 - 5) = 0.2
For 6, we have 1/12 × (10 - 5) = 0.41
For 7, we have 1/12 × (10 - 5) = 0.41
For 8, we have 1/12 × (10 - 5) = 0.41
For 9, we have 1/18 × (-20 - 5) = -1.3
For 10, we have 1/18 × (-20 - 5) = -1.3
For 11, we have 1/36 × (-20 - 5) = -0.69
For 12, we have 1/36 × (-25 - 5) = -0.69
The expected value of the winnings is given as follows;
0.41 + 0.41
+ 0.8
+ 0.8
+ 0.8
+ 0.41
+ 0.41
+ -1.3
-1.3 - 0.69
- 0.69
= -0.97
Therefore, the expected value = $-0.97, which is one is expected to lose $0.97
2) Using Microsoft Excel, we have;
The variance for the "winnings", σ² = $0.57966
3) The standard deviation for the "winnings" = √σ² = √(0.57966) ≈ $0.761354
4) The game is not a fair game because one is expected to lose $0.97
The number of compounding per year is
This can be calculated by making use of the formular; 920(1.03)^4t and use the compound interest equation which is N=P( 1+r/n)^nt
We know that 12% was given as the rate per year, then to get the quarter rate we divide by factor of 4, which is 12/4= 3%
The compounding for t years = n*t = 4t where n=4.
and the Initial number of cars serviced=920
Then we can substitute the values into the above equation, we have Thus
Learn more about compound interest at:
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CHECK THE COMPLETE QUESTION BELOW:
Drag the tiles to the boxes to form correct pairs. Not all tiles will be used. A car repair center services 920 cars in 2012. The number of cars serviced increases quarterly at a rate of 12% per year after 2012. Create an exponential expression to model the number of cars serviced after t years. Then, match each part of the exponential expression to what it represents in the context of the situation. 920(1.03) is the number of cars multiplied by 1.03. The quarterly rate of growth is 0.03 or 3%. The compound periods multiplied by the number of years is 4t. The initial number of cars serviced is 920. The growth factor is represented by 1.03. The growth rate is 1.03. Exponent arrowRight Base arrowRight Coefficient arrowRight Rate arrowRight