This is a Poisson distribution problem. The Poisson distribution gives the probability of a given number of events (in this case, cars crossing the roadway) happening in a fixed interval of time.

The formula for the Poisson probability is:

P(X=k) = (λ^k * e^-λ) / k!

where:
- λ is the average rate of occurrence (in this case, the average number of cars crossing the roadway per 5 minutes)
- e is the base of the natural logarithm (approximately 2.71828)
- k is the actual number of events

First, we need to find λ. We know that 30 cars cross the roadway every hour, so in 5 minutes (which is 1/12 of an hour), the average number of cars crossing is 30/12 = 2.5.

We want to find the probability that only one car will cross in the next 5 minutes, so k = 1.

Plugging these values into the formula, we get:

P(X=1) = (2.5^1 * e^-2.5) / 1! = 0.2052

So, the answer is A. 0.2052.

Question

This is a Poisson distribution problem. The Poisson distribution gives the probability of a given number of events (in this case, cars crossing the roadway) happening in a fixed interval of time.

The formula for the Poisson probability is:

P(X=k) = (λ^k * e^-λ) / k!

where:
- λ is the average rate of occurrence (in this case, the average number of cars crossing the roadway per 5 minutes)
- e is the base of the natural logarithm (approximately 2.71828)
- k is the actual number of events

First, we need to find λ. We know that 30 cars cross the roadway every hour, so in 5 minutes (which is 1/12 of an hour), the average number of cars crossing is 30/12 = 2.5.

We want to find the probability that only one car will cross in the next 5 minutes, so k = 1.

Plugging these values into the formula, we get:

P(X=1) = (2.5^1 * e^-2.5) / 1! = 0.2052

So, the answer is A. 0.2052.

Knowee AI · Accepted Answer

This is a Poisson distribution problem. The Poisson distribution gives the probability of a given number of events (in this case, cars crossing the roadway) happening in a fixed interval of time.

The formula for the Poisson probability is:

P(X=k) = (λ^k * e^-λ) / k!

where:
- λ is the average rate of occurrence (in this case, the average number of cars crossing the roadway per 5 minutes)
- e is the base of the natural logarithm (approximately 2.71828)
- k is the actual number of events

First, we need to find λ. We know that 30 cars cross the roadway every hour, so in 5 minutes (which is 1/12 of an hour), the average number of cars crossing is 30/12 = 2.5.

We want to find the probability that only one car will cross in the next 5 minutes, so k = 1.

Plugging these values into the formula, we get:

P(X=1) = (2.5^1 * e^-2.5) / 1! = 0.2052

So, the answer is A. 0.2052.

There are 30 cars crossing the roadway every hour. What is the probability that only one car will cross in next 5 minutes?A.0.2052B.0.9179

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