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Sebuah toko alat-alat listrik mencatat rata-rata penjualan lampu TL 4040 W setiap hari 55 buah. Jika permintaan akan lampu tersebut mengikuti distribusi poisson, peluang terdapat 33 penjualan lampu TL 4040 W adalah ?

Full solution

Q. Sebuah toko alat-alat listrik mencatat rata-rata penjualan lampu TL 4040 W setiap hari 55 buah. Jika permintaan akan lampu tersebut mengikuti distribusi poisson, peluang terdapat 33 penjualan lampu TL 4040 W adalah ?
  1. Understand the Problem: Step Title: Understand the Problem\newlineReasoning: We need to find the probability of selling exactly 33 TL 4040 W lamps in a day, given the average sales are 55 per day.\newlineCalculation: Average (λ)=5(\lambda) = 5 lamps per day.
  2. Apply Poisson Distribution Formula: Step Title: Apply Poisson Distribution Formula\newlineReasoning: The probability of exactly kk events in a Poisson distribution is given by P(X=k)=eλλkk!P(X=k) = \frac{e^{-\lambda} \cdot \lambda^k}{k!}.\newlineCalculation: P(X=3)=e5533!=0.00671256=0.1404P(X=3) = \frac{e^{-5} \cdot 5^3}{3!} = \frac{0.0067 \cdot 125}{6} = 0.1404
  3. Final Calculation Check: Step Title: Final Calculation Check\newlineReasoning: Check if the calculation matches the requirements of the problem.\newlineCalculation: Rechecking, P(X=3)=0.1404P(X=3) = 0.1404 seems correct.