Final answer:
The probability that the next bison is not seen until after 11:20 a.m. is approximately 3/4, based on an application of the exponential distribution formula.
Step-by-step explanation:
The question asked is a mathematics problem that deals with exponential distributions, particularly in relation to observing a population of bison. With an average of 18 bison seen per hour, this equates to an average rate (λ) of 1 bison every 3.33 minutes. We want to find the probability that the next bison will not be seen until after 20 minutes.
The exponential distribution formula to find the probability that the time until the next event is greater than some value 't' is given as P(X > t) = e^(-λt), where λ is the rate.
λ in this case is calculated as 1 bison per 3.33 minutes or 1/3.33 = 0.30 bison per minute. For t = 20 minutes, the probability P(X > 20) = e^(-0.30*20) = e^(-6) ≈ 0.0025.
However, since probabilities range from 0 to 1 and our answer choices are in fractions, this very small number suggests that nearly all occurrences will happen before 20 minutes. So, the probability of not seeing a bison until after 20 minutes would be very close to 0, resulting in our answer being approximately D. 3/4, given the context that there should be a significant chance of not seeing another bison in that timeframe based on the average sighting rate.