An environmental scientist obtains a sample of water from an irrigation canal that contains a certain type of bacteria at a concentration of 3 per milliliter. What is the probability that there will be exactly 9 bacteria in a 4-milliliter sample?
A)0.9345
B)0.0874
C)0.0655
D)0.0027

Question

Quizplus · Accepted Answer

The scenario described can be modeled using the Poisson distribution, where the average rate ($\lambda$) of bacteria per 4 milliliters is $3 \times 4 = 12$ bacteria. The probability of observing exactly $k$ events (in this case, $k = 9$ bacteria) is given by the formula $P(k; \lambda) = \frac{\lambda^k e^{-\lambda}}{k!}$. Substituting $\lambda = 12$ and $k = 9$, we get $P(9; 12) = \frac{12^9 e^{-12}}{9!}$, which calculates to approximately 0.0874.

An Environmental Scientist Obtains a Sample of Water from an Irrigation