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Chapter 5: Q5.4-2E (page 296)

Suppose that on a given weekend, the number of accidents at a certain intersection has the Poisson distribution with a mean of 0.7. What is the probability that there will be at least three accidents at the intersection during the weekend?

Short Answer

Expert verified

The probability of at least three accidents at the intersection during the weekend is 0.0342.

Step by step solution

01

Given information

The total number of accidents follows a Poisson distribution with a mean of 0.7.

02

Compute the probability

Let the total number of accidents at a certain intersection on a given weekend be denoted by X.

Then, the variable X has a Poisson distribution with a mean of 0.7.

The probability of occurring at least three accidents at the intersection during the weekend is

\(\begin{aligned}{c}P\left( {X \ge 3} \right) &= 0.0284 + 0.0050 + 0.0007 + 0.0001\\ &= 0.0342\end{aligned}\)

(Referring to the table of Poisson probabilities on page number 857 for the answer)

Therefore, the probability of occurring at least three accidents at the intersection during the weekend is 0.0342.

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