can please check my answer:
Q. 500 individuals tested a new biometric security system that will be used to verify that people attempting to enter a site are authorised to do so. 200 of the testers were authorised users and 300 were not. At one particular threshold the system shut out 10 individuals it should have admitted and admitted 2 individuals it should have shut out.Find out
a. What is the false match rate (FMR) of this system at this threshold?
b. What is the false non-match rate (FNMR) of this system at this threshold?
Answer a. 0.4% b. 3.33%
To check your answers, we need to calculate the false match rate (FMR) and the false non-match rate (FNMR) based on the information given.
Let's start with the false match rate (FMR):
False match rate (FMR) = (Number of individuals wrongly admitted / Total number of non-authorized testers) * 100
From the question, it is stated that the system admitted 2 individuals it should have shut out. The total number of non-authorized testers is 300.
FMR = (2 / 300) * 100 ≈ 0.67%
So the correct answer for part a is approximately 0.67%, not 0.4%.
Moving on to the false non-match rate (FNMR):
False non-match rate (FNMR) = (Number of individuals wrongly shut out / Total number of authorized testers) * 100
From the question, it is stated that the system shut out 10 individuals it should have admitted. The total number of authorized testers is 200.
FNMR = (10 / 200) * 100 = 5%
So the correct answer for part b is 5%, not 3.33%.
Therefore, the correct answers are:
a. The false match rate (FMR) of this system at this threshold is approximately 0.67%.
b. The false non-match rate (FNMR) of this system at this threshold is 5%.
To calculate the false match rate (FMR) and false non-match rate (FNMR), we need to determine the number of false matches and false non-matches, respectively.
To find the false match rate (FMR):
1. The system shut out 10 individuals it should have admitted. These 10 individuals are false matches.
2. To calculate the false match rate, divide the number of false matches (10) by the total number of non-authorized testers (300).
FMR = (Number of false matches / Total number of non-authorized testers) * 100
FMR = (10 / 300) * 100
FMR = 3.33%
Therefore, the false match rate (FMR) of this system at this threshold is 3.33%.
To find the false non-match rate (FNMR):
1. The system admitted 2 individuals it should have shut out. These 2 individuals are false non-matches.
2. To calculate the false non-match rate, divide the number of false non-matches (2) by the total number of authorized testers (200).
FNMR = (Number of false non-matches / Total number of authorized testers) * 100
FNMR = (2 / 200) * 100
FNMR = 1%
Therefore, the false non-match rate (FNMR) of this system at this threshold is 1%.
Note: The answers you provided (0.4% for FMR and 3.33% for FNMR) do not match the calculations based on the given information.