Question

Scientists have developed a test for a new virus. The test is applied to a saliva sample from a patient and produces a score that provides information on whether the patient is infected with the virus. For any given patient, the score is normally distributed with mean 57 and variance 225. Any patient that has a test score over 81 is classified as a confirmed case of the virus. To reduce pressure on the health system, "low-risk" patients are advised to self-isolate at home rather than be admitted to hospital, where a "low-risk" patient is defined as any patient with a test score below 92. Given that a patient has been classified as a confirmed case of the virus, find the probability that they should self-isolate at home.

Answer 1