Westonci.ca connects you with experts who provide insightful answers to your questions. Join us today and start learning! Connect with professionals ready to provide precise answers to your questions on our comprehensive Q&A platform. Experience the convenience of finding accurate answers to your questions from knowledgeable experts on our platform.
Sagot :
Using the Poisson distribution, there is a 0.8335 = 83.35% probability that 2 or fewer will be stolen.
What is the Poisson distribution?
In a Poisson distribution, the probability that X represents the number of successes of a random variable is given by:
[tex]P(X = x) = \frac{e^{-\mu}\mu^{x}}{(x)!}[/tex]
The parameters are:
- x is the number of successes
- e = 2.71828 is the Euler number
- [tex]\mu[/tex] is the mean in the given interval.
The probability that a rental car will be stolen is 0.0004, hence, for 3500 cars, the mean is:
[tex]\mu = 3500 \times 0.0004 = 1.4[/tex]
The probability that 2 or fewer cars will be stolen is:
[tex]P(X \leq 2) = P(X = 0) + P(X = 1) + P(X = 2)[/tex]
In which:
[tex]P(X = x) = \frac{e^{-\mu}\mu^{x}}{(x)!}[/tex]
[tex]P(X = 0) = \frac{e^{-1.4}1.4^{0}}{(0)!} = 0.2466[/tex]
[tex]P(X = 1) = \frac{e^{-1.4}1.4^{1}}{(1)!} = 0.3452[/tex]
[tex]P(X = 2) = \frac{e^{-1.4}1.4^{2}}{(2)!} = 0.2417[/tex]
Then:
[tex]P(X \leq 2) = P(X = 0) + P(X = 1) + P(X = 2) = 0.2466 + 0.3452 + 0.2417 = 0.8335[/tex]
0.8335 = 83.35% probability that 2 or fewer will be stolen.
More can be learned about the Poisson distribution at https://brainly.com/question/13971530
#SPJ1
We hope this information was helpful. Feel free to return anytime for more answers to your questions and concerns. Thanks for using our service. We're always here to provide accurate and up-to-date answers to all your queries. We're glad you chose Westonci.ca. Revisit us for updated answers from our knowledgeable team.
