Part A (streaming mean): A dataset has 1,000 observations with mean 12.4. You remove 50 observations whose mean is 20.1 and then append 30 new observations whose mean is 9.8. Without recomputing from raw data, what is the exact new mean? Show the formula you use and the final value to 3 decimal places. Part B (binomial vs Poisson): Let X ~ Binomial(n=40, p=0.07). 1) Compute P(X=0), P(X≤2), and P(X≥3) exactly (4 decimal places). 2) Approximate the same three quantities using a Poisson(λ = n·p) model with continuity where appropriate; report absolute errors for each quantity (|exact − approx|). 3) Briefly justify when the Poisson approximation is appropriate here and how you would tighten the approximation if p were larger.