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VLD [36.1K]
2 years ago
15

The number of traffic accidents occurring on any given day in Coralville is Poisson distributed with mean 5. The probability tha

t any such accidentinvolves an uninsured driver is 0.25, independent of all other such accidents.
Calculate the probability that on a given day in Coralville there are no trafficaccidents that involve an uninsured driver.



The answer is 0.278. Could you please explain why?
Mathematics
1 answer:
Nostrana [21]2 years ago
6 0

Answer:

The answer is 0.2865

Step-by-step explanation:

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

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

In which

x is the number of sucesses

e = 2.71828 is the Euler number

\mu is the mean in the given time interval.

In this problem, we have that:

The mean number of accidents on any given day in Coralville is 5. Of those, 25% are with an uninsured drive.

So \mu = 5*0.25 = 1.25

Calculate the probability that on a given day in Coralville there are no trafficaccidents that involve an uninsured driver.

This is P(X = 0). So

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

P(X = 0) = \frac{e^{-1.25}*(1.25)^{0}}{(0)!} = 02865

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