In 1943, Salvadore Luria and Max Delbrck did some pioneering research on bacterial genetics--specifically on the resistance of bacteria to viral attack. The research (years ahead of its time) is particularly relevant now because antibiotic resistance models may prove to be similar. Antibiotic resistance is proving to be one of the greatest threats to modern public health.

Suppose 69 colonies appeared on 60 plates. The mean number of colonies on a plate would be 69/60 or 1.15.

a. Assuming a Poisson distribution, calculate probability that there will be 0 colonies on a plate. Repeat the calculation for one colony, two colonies, three colonies and four colonies.

b. What is mean and the standard deviation for the number of colonies on a plate?

c. What is the probability that there will be four or more colonies on a plate?