An incubation period is the time it takes for an infection to develop after a person has been exposed to a disease causing organism. The incubation period for COVID-19 is normally distributed with a mean incubation period of 7.5 days and a standard deviation of 1.5 days.

a) Draw a sketch of this normal distribution labelling the mean and the values that are one, two, and three standard deviation above/below the mean on the horizontal axis.

b) Suppose a person who contracted COVID-19 is selected at random. What is the probability that they have an incubation period between 4.5 and 9 days?

c) People who come into contact with the virus are told to isolate until the incubation period has passed, since symptoms are often not present during the virus's incubation stage. If no symptoms emerge, we assume they did not contract the virus; if symptoms do emerge we assume that the virus was transmitted.

I. One healthcare team states that we need 97.5% of infected individuals to isolate in order to prevent widespread community transmission. If we were to take this advice how long should the suggested isolation period be?

II. A second healthcare team states that we only need 84% of infected individuals to isolate to prevent widespread community transmission. If we were to take this advice how long should the suggested isolation period be?

d) The local government is advising people who came into contact with the virus to isolate for 6 days. We will assume that every person follows this advice.

I. What percentage of people will end their isolation prematurely (i.e. before their symptoms present)?

II. Assuming 500 people become infected, how many of them will leave isolation prematurely? [1