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Sebuah toko alat-alat listrik mencatat rata-rata penjualan lampu TL $40\,\text{W}$ setiap hari $5$ buah. Jika permintaan akan lampu tersebut mengikuti distribusi poisson, peluang terdapat lebih dari $2$ penjualan lampu TL $40\,\text{W}$ adalah ?

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Factor polynomials

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Q. Sebuah toko alat-alat listrik mencatat rata-rata penjualan lampu TL

40\,\text{W}

setiap hari

5

buah. Jika permintaan akan lampu tersebut mengikuti distribusi poisson, peluang terdapat lebih dari

2

penjualan lampu TL

40\,\text{W}

adalah ?

Understand the Distribution: Step Title: Understand the Distribution $\newline$ Concise Step Description: Recognize that the problem follows a Poisson distribution with a mean $\lambda$ of $5$ . $\newline$ Step Calculation: $\lambda = 5$ $\newline$ Step Output: Poisson distribution with $\lambda = 5$
Calculate the Probability: Step Title: Calculate the Probability $\newline$ Concise Step Description: Use the Poisson formula to find the probability of more than $2$ sales, which is $1$ minus the probability of $0$ , $1$ , or $2$ sales. $\newline$ Step Calculation: $P(X > 2) = 1 - (P(X=0) + P(X=1) + P(X=2))$ $\newline$ $P(X=0) = e^{-5} \times 5^0 / 0! = 0.0067$ $\newline$ $P(X=1) = e^{-5} \times 5^1 / 1! = 0.0337$ $\newline$ $P(X=2) = e^{-5} \times 5^2 / 2! = 0.0842$ $\newline$ $P(X > 2) = 1 - (0.0067 + 0.0337 + 0.0842) = 0.8754$ $\newline$ Step Output: Probability of more than $2$ sales is $0.8754$

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