Cysts ​ After Researching Cysts of a Particular Type,a Doctor

question 33

Essay

Cysts
​ After researching cysts of a particular type,a doctor learns that out of 10,000 such cysts examined,1,500 are malignant and 8,500 are benign.A diagnostic test is available which is accurate 80% of the time (whether the cyst is malignant or not).The doctor has discovered the same type of cyst in a patient. ​ ​
-{Cysts Narrative} What is the probability that the patient will test positive?

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Definitions:

Error Variable

A variable in statistical models that represents the deviation of observed values from the predicted values, reflecting unexplained or random variation.

Normal

Referring to a bell-shaped distribution that is symmetric about its mean, used in statistics to describe well-behaved data sets.

Total Variation

The overall measure of the spread or dispersion of a set of data points from the mean or expected value.

SSR

Sum of Squares due to Regression, a measure used in statistical analysis to determine the variation explained by the independent variable(s) in a regression model.