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Mila [183]
3 years ago
8

A certain genetic condition affects 8% of the population in a city of 10,000. Suppose there is a test for the condition that has

an error rate of 1% (i.e., 1% false negatives and 1% false positives).
Consider the values that would complete the table below.

Has condition Does not have condition totals

Test positive

Test negative

Totals

What is the probability (as a percentage) that a person has the condition if he or she tests positive? (Round your answer to one decimal place.)
Mathematics
1 answer:
enot [183]3 years ago
7 0

Solution:

Population in the city= 10,000

As genetic condition affects 8% of the population.

8 % of 10,000

=\frac{8}{100}\times 10,000=800

As, it is also given that, there is an error rate of 1% for condition (i.e., 1% false negatives and 1% false positives).

So, 1% false negatives means out of 800 tested who are found affected , means there are chances that 1% who was found affected are not affected at all.

So, 1% of 800 =\frac{1}{100}\times 800=8

Also,  1% false positives means out of 10,000 tested,[10,000-800= 9200] who are found not affected , means there are chances that 1% who was found not affected can be affected also.

So, 1% of 9200 =\frac{1}{100}\times 9200=92

1. Has condition Does not have condition totals  = 800

2. Test positive =92

3. Test negative =8

4. Total =800 +92 +8=900

5. Probability (as a percentage) that a person has the condition if he or she tests positive= As 8% are found positive among 10,000 means 9200 are not found affected.But there are chances that out of 9200 , 1% may be affected

=\frac{\text{1 percent of 9200}}{9200}\\\\ \frac{\frac{1}{100}\times 9200}{9200}=\frac{92}{9200}\\\\ =0.01

that is Probability equal to 0.01 or 1%.

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Answer:

Option C.

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Step-by-step explanation:

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The distance between the circle and the point will be the difference of the distance of the point from the center of circle  and the radius of the circle

step 1

Find the center and radius of the circle

we have

x^{2} +y^{2}-8y=0

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x^{2} +(y^{2}-8y+16)=0+16

Rewrite as perfect squares

x^{2} +(y-4)^{2}=16

so

The center is the point (0,4)

The radius is

r^{2}=16\\r=4\ units

step 2

Find the distance of the point from the center of circle

the formula to calculate the distance between two points is equal to

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we have

(6,-4) and (0,4)

substitute the values

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step 3

Find the difference of the distance of the point from the center of circle  and the radius of the circle

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therefore

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see the attached figure to better understand the problem

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