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 μ = 15.
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Explanation:
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 μ = 15.
a) If the area of the agar plate is 75 square centimeters (cm2), what is the probability of observing fewer than 4 CFUs in a 25 cm2 area of the plate? (Round your answer to four decimal places.)
(b) If you were to count the total number of CFUs in 5 plates, what is the probability you would observe more than 95 CFUs? Use the Poisson distribution to obtain this probability. (Round your answer to four decimal places.)
(c) Repeat the probability calculation in part (b) but now use the normal approximation. (Round your answer to four decimal )
(d)Find the difference between this value and your answer in part (b). (Round your answer to four decimal places.)