Normal distribution... - (Jan/04/2011 )
I'm doing probability exercises and I found one that relates the normal distribution with sensitivity and specificity, and I do not know how to solve it.
A continuous random variable in a healthy population is distributed according to N (12.1, 1.3). In a diseased population is distributed according to N (15.8, 1.5).
What is the value of the variable to be taken as the cutoff point for a sensitivity equal to 0.73?
What for a specificity of 0.93?
The only thing I can think of is to consider both the values of specificity and sensitivity as numbers Z and, apart from the formula of standardization, remove "x", which would be the respective cutoff points.
But I have no idea.
Could someone help me?
From my reading of the problem I get:
Sensitivity = 0.73= 1/(1+0.37) ie 37% false negatives
From Z-tables with N(15.8,1.5); 37% of the area is below 15.30
Specificity = 0.93 = 1/(1+0.075) ie 7.5% false positives
From Z-tables with N(12.1,1.3); 7.5% of the area is above 13.97