Final answer:
To find P(X > 1), use the Poisson distribution formula to calculate the probabilities of having 0 or 1 pit in a 1 cm^2 area. Subtract the sum of these probabilities from 1 to get P(X > 1).
Step-by-step explanation:
To find P(X > 1), we need to calculate the probability of having more than 1 pit in a 1 cm^2 area. This is equivalent to calculating 1 minus the probability of having 0 or 1 pit in a 1 cm^2 area.
The Poisson distribution formula is P(X = k) = (e^-λ * λ^k) / k!, where λ is the mean of the distribution.
In this case, the mean is 7, so we can calculate P(X = 0) and P(X = 1) and subtract the sum from 1 to get P(X > 1).
P(X = 0) = (e^-7 * 7^0) / 0! = e^-7 ≈ 0.000911
P(X = 1) = (e^-7 * 7^1) / 1! = 7e^-7 ≈ 0.00638
Therefore, P(X > 1) = 1 - (P(X = 0) + P(X = 1)) ≈ 1 - (0.000911 + 0.00638) = 0.9927