Laporan kejahatan yang dikeluarkan kepolisian menunjukkan terdapat $3.1$ pencurian motor per menit di Indonesia. Berapakah peluang terjadi tepat empat pencurian dalam menit tertentu ?

Full solution

Q. Laporan kejahatan yang dikeluarkan kepolisian menunjukkan terdapat

3.1

pencurian motor per menit di Indonesia. Berapakah peluang terjadi tepat empat pencurian dalam menit tertentu ?

Identify Distribution Type: Step Title: Identify the Distribution Type $\newline$ Short Reasoning: The problem describes the number of motorbike thefts per minute, which fits a Poisson distribution model because it counts the number of times an event happens in a fixed interval. $\newline$ Calculation: Recognize the problem as a Poisson distribution scenario.
Calculate Poisson Probability: Step Title: Calculate the Poisson Probability $\newline$ Short Reasoning: Use the Poisson formula $P(X=k) = \frac{e^{-\lambda} \cdot \lambda^k}{k!}$ where $\lambda$ is the average rate ( $3.1$ thefts/minute) and $k$ is the number of events ( $4$ thefts). $\newline$ Calculation: $P(X=4) = \frac{e^{-3.1} \cdot 3.1^4}{4!}$
Perform the Calculation: Step Title: Perform the Calculation $\newline$ Short Reasoning: Plug the values into the formula to find the probability. $\newline$ Calculation: $P(X=4) = (e^{-3.1} \times 3.1^4) / 24 = (0.045 \times 92.3521) / 24 = 0.174$