A land surveyor places two stakes 500 ft apart and creates a perpendicular to the line that connects these two stakes. He needs
2 answers:
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1) 4.55
2) Short hit
Step-by-step explanation:
1)
The score and corresponding probabilities are shown in the following table:
Score 3 4 5 6 7
Probability 0.15 0.40 0.25 0.15 0.05
Let us define
X = Miguel's score on the Water Hole
The expected value of the variable X can be represented as:
where
represents the different possible outcomes of X
denotes the associated probabilities
Accordingly, the expected value of Miguel's score is calculated as follows:
2)
Here, we will again consider:
X = Miguel's score on the Water Hole
In this case:
- For a successful long hit, the expected value of X is
- Conversely, if the long hit isn't successful, the expected value of X becomes
We also know that the likelihood of succeeding with a long hit is
Consequently, the chance of failure in a long hit is
Thus, the expected value of X when opting for the long hit strategy is:
In the first part of this question, we calculated the expected value using the short hit strategy, yielding:
Given that the expected value for X is smaller (which is better) when utilizing the short hit option, we can conclude that this approach is superior.