Final answer:
The incorrect statement about the Poisson arrival rate is λ = 20 arrivals per hour, as this contradicts the given arrival rate of one every 20 minutes. The correct rates are 3 arrivals per hour, 1/20 arrivals per minute, and 72 arrivals per day.
Step-by-step explanation:
If arrivals occur according to the Poisson distribution every 20 minutes, we can identify the incorrect statement among the given options. Let's first establish the correct rate of arrival, which is given as one arrival every 20 minutes.
Converting this to an hourly rate, we get that there are 3 arrivals per hour since 60 minutes divided by 20 equals 3. Thus, λ = 3 arrivals per hour is correct.
When considering the rate per minute, since there is one arrival every 20 minutes, we should divide one by 20, which results in λ = 1/20 arrivals per minute. This is also correct.
To find the rate per day (consisting of 24 hours), we would multiply the hourly rate by the number of hours in a day. So, 3 arrivals per hour times 24 hours equals 72 arrivals per day, which is also correct.
The incorrect statement is, therefore, λ = 20 arrivals per hour, as this suggests there is one arrival every 3 minutes, which contradicts the one arrival every 20 minutes as per the question.