Suppose that it is known that a certain disease occurs in 4% of the population. Suppose also that we have a certain medical test to determine if person has this disease. The test produces a positive reading on 99.4% of those infected with the disease. Suppose that this test gives a positive result in healthy patients 2% of the time. Assume we have 100,000 random individuals that follow the above information perfectly. Determine the number of false positives. Type your numeric answer and submit
Contingency Table
A contingency table can be defined as the visual representation of the relationship between two or more categorical variables that can be evaluated and registered. It is a categorical version of the scatterplot, which is used to investigate the linear relationship between two variables. A contingency table is indeed a type of frequency distribution table that displays two variables at the same time.
Binomial Distribution
Binomial is an algebraic expression of the sum or the difference of two terms. Before knowing about binomial distribution, we must know about the binomial theorem.
Information in question is given in terms of percentages or probability , so we will use this information to calculate probability by :
Number of false positives = Number of healthy individuals Probability of False positive
Number of false positives would depend on the number of healthy individuals only. Because among number of healthy individuals, we can get false positive.
P[false positive ]= P[positive result given person is healthy]
= 0.02
Also, among 100,000 random individuals, 100-4=96% of the individuals would be healthy, so,
number of healthy individuals is 100,00096/100=96,000
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