Answer:
The number of planes that land in a given time period follows a Poisson distribution with parameter lambda equal to the average rate of landing per unit time. In this case, lambda is equal to 0.1 planes per minute.
The probability that between 2 and 6 planes will land in 10 minutes is given by the cumulative distribution function of the Poisson distribution:
P(2 <= X <= 6) = P(X <= 6) - P(X <= 1)
Where X is the number of planes that land in 10 minutes.
Using the cumulative distribution function for the Poisson distribution, we have:
P(X <= 6) = 1 - e^(-0.1 * 10) * (1 + 0.1 * 10 + (0.1 * 10)^2 / 2! + ... + (0.1 * 10)^6 / 6!)
P(X <= 1) = 1 - e^(-0.1 * 10) * (1 + 0.1 * 10)
Therefore,
P(2 <= X <= 6) = (1 - e^(-0.1 * 10) * (1 + 0.1 * 10 + (0.1 * 10)^2 / 2! + ... + (0.1 * 10)^6 / 6!)) - (1 - e^(-0.1 * 10) * (1 + 0.1 * 10))
The exact value of this probability can be calculated using a calculator or computer software.