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valentina_108 [34]
1 year ago
8

The probability that a rental car will be stolen is. 4. if 3500 cars are rented, what is the approximate poisson probability tha

t 2 or fewer will be stolen?
Mathematics
1 answer:
kozerog [31]1 year ago
4 0

Using the Poisson distribution, there is a 0.8335 = 83.35% probability that 2 or fewer will be stolen.

<h3>What is the Poisson distribution?</h3>

In a Poisson distribution, the probability that X represents the number of successes of a random variable is given by:

P(X = x) = \frac{e^{-\mu}\mu^{x}}{(x)!}

The parameters are:

  • x is the number of successes
  • e = 2.71828 is the Euler number
  • \mu 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:

\mu = 3500 \times 0.0004 = 1.4

The probability that 2 or fewer cars will be stolen is:

P(X \leq 2) = P(X = 0) + P(X = 1) + P(X = 2)

In which:

P(X = x) = \frac{e^{-\mu}\mu^{x}}{(x)!}

P(X = 0) = \frac{e^{-1.4}1.4^{0}}{(0)!} = 0.2466

P(X = 1) = \frac{e^{-1.4}1.4^{1}}{(1)!} = 0.3452

P(X = 2) = \frac{e^{-1.4}1.4^{2}}{(2)!} = 0.2417

Then:

P(X \leq 2) = P(X = 0) + P(X = 1) + P(X = 2) = 0.2466 + 0.3452 + 0.2417 = 0.8335

0.8335 = 83.35% probability that 2 or fewer will be stolen.

More can be learned about the Poisson distribution at brainly.com/question/13971530

#SPJ1

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