The prostate-specific antigen (PSA) test is a simple blood test to screen for prostate cancer. It has been used in men over 50 a
s a routine part of a physical exam, with levels above 4 ng/mL indicating possible prostate cancer. The test result is not always correct, sometimes indicating prostate cancer when it is not present and often missing prostate cancer that is present. Suppose that these are the approximate conditional probabilities of a positive (above 4 ng/ml) and negative test result given cancer is present or absent. In a large study of prostate cancer screening, it was found that about 6.2% of the population has prostate cancer. Draw a tree diagram for selecting a person from this population (outcomes: cancer present or absent) and testing his blood (outcomes: test positive or negative).
1 answer:
The missing table for the Test Result can be expressed as:
Test Result
Positive Negative
Cancer Present 0.21 0.79
Cancer Absent 0.06 0.94
Answer:
Step-by-step explanation:
A tree diagram is an elegant way of determining an exhaustive list of sample elements in the sample space. It is by finding the ordered n-tuples of the elements in the events under consideration.
The tree diagram for selecting a person from the population in the given question can be found in the attached image below.
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Answer:
The rule that represents the function is therefore the function is
Step-by-step explanation:
We have 5 ordered pairs in the plane xy. This means that <em>every pair has the form (x, y).</em>
Then, we have 5 values of x, which will give us 5 values of y, using the rule that represents the function.
<u>The easy evaluation is that when x=0, the value of y is y=1,</u> and then we can evaluate the rule for x=-1, and x=1, <em>the value of y is the same, y=2</em>. We can see here that we have a parabolic function, that is not centered in the origin of coordinates because when x=0, y=1.
So <u>we propose the rule </u><u> which is correct for the first 3 values of x.</u>
Now, <em>we evaluate the proposed rule when x=2, and when x=3</em>. This evaluations can be written as
Therefore, the rule is correct, and the function is