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Answer :
The value of (200) f(200) is 0.25, indicating a 25% probability for a $200,000 profit. MRA has a 70% chance of being profitable and a 35% chance of making at least $100,000.
To find the missing value f(200) in the probability distribution table, we can use the fact that the sum of all probabilities in a probability distribution must equal 1. Given the provided probabilities for the profits, the sum of the known probabilities is 0.05 + 0.15 + 0.20 + 0.10 + 0.25 = 0.75. Therefore, the missing value can be found by subtracting the sum of the known probabilities from 1: 1 - 0.75 = 0.25. So, f(200) = 0.25.
The interpretation of this value is that there is a 25% probability that the MRA Company will make a profit of $200,000 in the first year of operation.
To find the probability that MRA will be profitable, we sum the probabilities for profits greater than zero: 0.15 + 0.20 + 0.10 + 0.25 = 0.70, meaning there is a 70% chance of profitability.
The probability that MRA will make at least $100,000 is the sum of probabilities for profits greater than or equal to $100,000: 0.10 + 0.25 = 0.35, indicating a 35% chance of achieving this profit level.
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Complete Question:
The following table is a partial probability distribution for the MRA Company's projected profits (x = profit in $1,000s) for the first year of operation (the negative value denotes a loss).
x f(x)
-100 0.05
0 0.15
50 0.20
100 0.10
150 0.25
200 ?
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