To solve this problem, we need to understand that the Poisson distribution is used for counting the number of times an event occurs in a given time period. The parameter of the Poisson distribution is the average number of events in that time period.

In this case, the average number of accidents in a 12-hour period is 2. Therefore, the average number of accidents in a 1-hour period would be 2/12 = 1/6.

The formula for the Poisson distribution is:

P(X=k) = (λ^k * e^-λ) / k!

where:
- P(X=k) is the probability of k events occurring in an interval,
- λ is the average rate of value,
- e is the base of the natural logarithm (approximately equal to 2.71828),
- k! is the factorial of k.

We want to find the probability that there will be no accidents in a 1-hour period, so we set k=0.

Substituting these values into the formula, we get:

P(X=0) = ((1/6)^0 * e^-(1/6)) / 0!
= (1 * e^-(1/6)) / 1
= e^-(1/6)
≈ 0.8465

So, the probability that there will be no accidents in a 1-hour period is approximately 0.8465, or 84.65%.

Question

To solve this problem, we need to understand that the Poisson distribution is used for counting the number of times an event occurs in a given time period. The parameter of the Poisson distribution is the average number of events in that time period.

In this case, the average number of accidents in a 12-hour period is 2. Therefore, the average number of accidents in a 1-hour period would be 2/12 = 1/6.

The formula for the Poisson distribution is:

P(X=k) = (λ^k * e^-λ) / k!

where:
- P(X=k) is the probability of k events occurring in an interval,
- λ is the average rate of value,
- e is the base of the natural logarithm (approximately equal to 2.71828),
- k! is the factorial of k.

We want to find the probability that there will be no accidents in a 1-hour period, so we set k=0.

Substituting these values into the formula, we get:

P(X=0) = ((1/6)^0 * e^-(1/6)) / 0!
       = (1 * e^-(1/6)) / 1
       = e^-(1/6)
       ≈ 0.8465

So, the probability that there will be no accidents in a 1-hour period is approximately 0.8465, or 84.65%.

Knowee AI · Accepted Answer

To solve this problem, we need to understand that the Poisson distribution is used for counting the number of times an event occurs in a given time period. The parameter of the Poisson distribution is the average number of events in that time period.

In this case, the average number of accidents in a 12-hour period is 2. Therefore, the average number of accidents in a 1-hour period would be 2/12 = 1/6.

The formula for the Poisson distribution is:

P(X=k) = (λ^k * e^-λ) / k!

where:
- P(X=k) is the probability of k events occurring in an interval,
- λ is the average rate of value,
- e is the base of the natural logarithm (approximately equal to 2.71828),
- k! is the factorial of k.

We want to find the probability that there will be no accidents in a 1-hour period, so we set k=0.

Substituting these values into the formula, we get:

P(X=0) = ((1/6)^0 * e^-(1/6)) / 0!
       = (1 * e^-(1/6)) / 1
       = e^-(1/6)
       ≈ 0.8465

So, the probability that there will be no accidents in a 1-hour period is approximately 0.8465, or 84.65%.

The number of accidents (𝐴) at an intersection is counted for a 12-hour period. The number of accidents follows a Poisson distribution with a parameter value of 2.Calculate the probability that there will be no accidents in a 1-hour period.

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