Final answer:
To calculate the probability P(X≤2) for a Poisson distribution with λ=3.0, we use the given complementary probability P(X > 3)=0.3528 to find P(X≤3) which is also P(X≤2), resulting in a probability of 0.6472.
Step-by-step explanation:
Calculating Poisson Probability for X≤2
To find the probability P(X≤2), given that X is a Poisson random variable with mean λ = 3.0, we can use the complementary probability and the cumulative Poisson probability function. Since we are given that P(X > 3) = 0.3528, we can deduce that P(X ≤ 3) = 1 - P(X > 3) = 1 - 0.3528 = 0.6472. Based on this information and understanding that Poisson probabilities are inclusive of their upper bound (due to the nature of discrete probability distributions), P(X≤2) = P(X≤3). Therefore:
P(X≤2) = P(X≤3) = 0.6472 (using the complementary probability provided)
Note: Depending on the context and whether more specific calculations are needed using a Poisson probability distribution calculator or tables, further calculation steps might be required.