Number of colony-forming units. In microbiology,

Problem 5.74

In microbiology, colony-forming units (CFUs) are used to measure the number of microorganisms present in a sample. To determine the number of CFUs, the sample is prepared, spread uniformly on an agar plate, and then incubated at some suitable temperature. Suppose that the number of CFUs that appear after incubation follows a Poisson distribution with 15.

(a) If the area of the agar plate is 75 square centimetres , what is the probability of observing fewer than 4 CFUs in a 25  area of the plate?

(b) If you were to count the total number of CFUs in 5 plates, what is the probability you would observe more than 90 CFUs? Use the Poisson distribution to obtain this probability.

(c) Repeat the probability calculation in part (b) but now use the Normal approximation. How close is your answer to your answer in part (b)?

                                                               Step by Step Solution

Step 1 of 3

(a) In microbiology, colony-forming units (CFUs) are used to measure the number of microorganisms present in a sample. To determine the number of CFUs, the sample is prepared, spread uniformly on an agar plate, and then incubated at some suitable temperature. Suppose that the number of CFUs that appear after incubation follows a Poisson distribution with .

The area of the agar plate is 75 square centimetres.

To determine the probability of observing fewer than 4 CFUs in a 25 square centimetres area of the plate

The mean of CFUs appearing in a 25 square centimetres area is

Then,

Hence, the probability of observing fewer than 4 CFUs in a 25 square centimetres area of the plate is 0.26502.