The difference of the range and the interquartile range of the data set represented by the box plot is
2 answers:
Answer:
Step-by-step explanation:
The interquartile range is IQR is:
Where:
= third quartile
= first quartile
So the interquartile range is the difference between the highest quartile and the lowest quartile. In other words, it is the width of the box in the diagram.
So:
The R range is the difference between the highest value and the lowest. In other words:
Finally:
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2) Short hit
Step-by-step explanation:
1)
The table containing the score and the relative probability of each score is:
Score 3 4 5 6 7
Probability 0.15 0.40 0.25 0.15 0.05
Here we call
X = Miguel's score on the Water Hole
The expected value of a certain variable X is given by:
where
are all the possible values that the variable X can take
is the probability that
Therefore in this problem, the expected value of MIguel's score is given by:
2)
In this problem, we call:
X = Miguel's score on the Water Hole
Here we have that:
- If the long hit is successfull, the expected value of X is
- Instead, if the long hit fails, the expected value of X is
Here we also know that the probability of a successfull long hit is
Which means that the probabilty of an unsuccessfull long hit is
Therefore, the expected value of X if Miguel chooses the long hit approach is:
In part 1) of the problem, we saw that the expected value for the short hit was instead
Since the expected value for X is lower (=better) for the short hit approach, we can say that the short hit approach is better.