QUESTION 1

Suppose that a Covid-19 testing centre receives two phones calls, on average, per minute concerning test results.

Required:

a) What are the conditions for this experiment to be considered a Poisson experiment? Motivate.

b) What is the expected number of phone calls regarding test results per hour?

c) What is the probability that more zero but less than four phone calls regarding test results are received in any given period of two minutes?

d) What is the probability that more than one phone calls regarding test results are received in any given period of three minutes?

e) What is the probability that no phone calls regarding test results are received in any given period of one minute?

Question 2

Suppose that a random variable X is normally distributed with a mean of 200 and a variance of 625.

Required:

a) What proportion of X-values lies between 180 and 195?

b) Below what value do 33 per cent of X-values lie?

c) What proportion of X-values are more than 190?

d) What proportion of X-values are less than 195?