Final answer:
To determine the probabilities of cars arriving at McDonald's drive-thru using the Poisson distribution, we utilize the formula P(X = x) for the exact number of arrivals and 1 minus the cumulative probability up to x for more than x arrivals.
Step-by-step explanation:
The question asks about determining probabilities related to the arrival of cars at McDonald's drive-thru using the exponential distribution, a concept from statistics within mathematics. Specifically, we are to find the probability of exactly x cars arriving in an hour and the probability of more than x cars arriving within the same timeframe, given a rate of 20 cars per hour.
To calculate these probabilities, we typically use the formula for the Poisson distribution, which is suitable for modeling the number of times an event (in this case, the arrival of a car) occurs in a fixed interval of time or space if these events happen with a known constant rate and independently of the time since the last event.
- To find the probability that exactly x cars will arrive, we use the formula: P(X = x) = (e-λ * λx)/x!, where λ is the average rate of occurrence (20 cars per hour) and x is the number of cars.
- To find the probability that more than x cars will arrive, we calculate 1 minus the cumulative probability of x cars arriving. This can be done by summing the individual Poisson probabilities from 0 to x and subtracting from 1.