Consider two tumor markers for lung cancer, CYFRA 21-1 and CEA, which tend to be elevated in patients with lung cancer relative to those with benign lung disease. A study was conducted on patients with known lung cancer status to assess how these tumor markers could be used for clinical diagnosis. The study team observed that in patients with lung cancer, CYFRA 21-1 is normally distributed with mean 4.7 ng/mL and standard deviation 9.2 ng/mL while CEA is normally distributed with mean 5.9 ng/mL and standard deviation 19.8 ng/mL. In patients with benign lung disease, CYFRA 21-1 is normally distributed with mean 1.6 ng/mL and standard deviation 4.3 ng/mL while CEA is normally distributed with mean 2.2 ng/mL and standard deviation 5.3 ng/mL.

The study team is interested in whether a diagnostic test based on both CYFRA 21-1 and CEA is an improvement over tests based solely on one of the markers. Suppose that a patient is classified as having lung cancer if a patient tests positive for lung cancer if CYFRA 21-1 level is greater than 3.3 ng/mL, or CEA level is greater than 5.0 ng/mL, or both are elevated.

Compute the sensitivity and specificity of this diagnostic test.