Probability Distribution Problem

In summary, the conversation discusses the probability of no cars passing an intersection during a three-minute interval, given that cars pass at a rate of 30 miles per hour. The use of a Poisson distribution is considered, but it is noted that the average number of cars passing the intersection is not specified.
  • #1
joypav
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Suppose that cars pass a certain intersection at a rate of 30 miles per hour. What is the probability that during a three-minute interval, no cars will pass the intersection?

I am really just wondering which distribution to use. I thought is should be Poisson because it is asking for events occurring during a certain time period. But it doesn't say how many cars pass the intersection on average?
 
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  • #2
joypav said:
Suppose that cars pass a certain intersection at a rate of 30 miles per hour. What is the probability that during a three-minute interval, no cars will pass the intersection?

I am really just wondering which distribution to use. I thought is should be Poisson because it is asking for events occurring during a certain time period. But it doesn't say how many cars pass the intersection on average?
I think you mean 30 cars per hour, not 30 miles per hour. The speed at which the cars pass does not seem to be relevant.

If it's 30 cars per hour, then on average a car passes every 2 minutes. You should be able to use this to construct a Poisson distribution to model the flow of traffic.
 
  • #3
My review definitely says miles per hour. I was thinking it may be a typo too, but wanted to make sure I wasn't just misunderstanding. Thank you
 

FAQ: Probability Distribution Problem

What is a probability distribution problem?

A probability distribution problem is a mathematical problem that involves determining the likelihood of different outcomes or events occurring. It is based on the principles of probability and can be used to analyze data and make predictions.

What are the different types of probability distributions?

There are several types of probability distributions, including the normal distribution, binomial distribution, Poisson distribution, and exponential distribution. Each type has its own characteristics and uses.

How is a probability distribution represented?

A probability distribution can be represented in several ways, such as a graph, a table, or a mathematical equation. The most common way to represent a probability distribution is through a graph, where the x-axis represents the possible outcomes and the y-axis represents the probability of each outcome.

How do you calculate the mean and standard deviation of a probability distribution?

The mean of a probability distribution is calculated by multiplying each possible outcome by its corresponding probability and then summing the results. The standard deviation is calculated by taking the square root of the variance, which is the sum of the squared differences between each outcome and the mean.

How can probability distributions be used in real-life situations?

Probability distributions can be used in a variety of real-life situations, such as predicting stock market trends, analyzing data in scientific studies, and making decisions in gambling or risk management. They can also be used to model and understand natural phenomena, such as the distribution of animal populations or the occurrence of natural disasters.

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