1) Scientists are developing a test for a new virus that is based on measuring a person's antibody levels. The test produces a score that provides information on whether the person is infected with the virus. For any given person, the score is normally distributed with mean 64 and variance 196. Assume that the test scores are independent from person to person. Any person with a test score over 76 is considered a confirmed case of the virus. In a random sample of 12 people, each person was given the antibody test. Find the probability that more than 2 people in the sample will be confirmed to have the virus.

2)When a saliva sample is collected from a patient to test for the presence of a new virus, occasionally the sample does not contain enough of the virus' genetic material to be viable for testing. Suppose the probability that any given sample is viable for testing is 0.31 and that the viability of a sample is independent from sample to sample. For a random selection of 10 saliva samples, given that more than 2 samples were found to be viable, find the probability that less than 4 samples were viable.