1) A certain protein is present in everyones saliva, but Covid 19 increases its concentration. An instant test is developed 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 2 units/ml. For people with covid 19 the protein has a concentration 23 units/ml and standard deviation of 1 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.

i) Using Tchebychev's rule

a) What is the maximum probability of falsely labelling a healthy person as having covid 19? *(show work on all problems)

b)What is the maximum probability of incorrectly saying a person does not covid 19 when they do?