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A certain protein is present in everyones saliva, but Covid 19 increases its concentration. An instant test is develeped based on this measuring this protein: For people without covid 19, the protein has a concentration with a mean of 9 units/ml, and a standard deviation of 3 units/ml. For people with covid 19 the protein has a concentration 23 units/ml and standard deviation of 2 unit/ml Suppose we set a cutoff value of the test at 19 units/ml. So above 19 units/ml they are considered to have covid 19, and below 19 units they are not.
Assuming the two distributions are normal:
a) What is the probability of falsely labelling a healthy person as having covid 19?
b) What is the probability of correctly saying a person does have covid 19 when they do?
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