Probability of Poisson Distribution: Nr of Customers in Shop

In summary, the conversation discussed the arrival rate of customers at a shop, which follows a Poisson distribution. The probability of at least 5 more minutes passing before the next customer arrives was found to be 0.2636. The probability of having at least 7 and at most 15 intervals out of 40 with at most 2 customers arriving was calculated using the binomial distribution and found to be 0.855. The concept of memorylessness was also briefly mentioned.
  • #1
pinto89a
5
0
Nr of customers arriving at a shop follow Poisson.
In 15, an average of 4 customers arrive.

a)
A customer has just arrived. Then a minute passed and no one arrived. What is the probability of it takoing at least 5 more min. until another customer arrives?

b)
Consider 40 non-overlapping periods of 15 min.

What is the probability that
at least 7 and at most 15 of those intervals have at most 2 customers arriving?

In book, answer to
a) is 0.2636
b) is F(2.22) - F(-1.12) = 0.855

In a) although I don't see why, I understande that it's something about memorylessness or something. But how do you get to the answer in question b)?
 
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  • #2
pinto89a said:
how do you get to the answer in question b)?

via binomial distribution
 
  • #3
Ok, I see now.Thank you.
 

Related to Probability of Poisson Distribution: Nr of Customers in Shop

1. What is a Poisson distribution?

A Poisson distribution is a statistical distribution that is used to model the probability of a certain number of events occurring within a specific time or space when the events are independent and the average rate of occurrence is known.

2. How is the Poisson distribution used to calculate the probability of number of customers in a shop?

The Poisson distribution can be used to calculate the probability of a specific number of customers in a shop by using the average rate of customer arrivals as the parameter λ and plugging in the desired number of customers into the probability mass function formula.

3. What is the difference between the Poisson distribution and the normal distribution?

The Poisson distribution is used for discrete random variables, while the normal distribution is used for continuous random variables. Additionally, the Poisson distribution is used to model rare events, while the normal distribution is used for more common events.

4. Can the Poisson distribution be used for any type of event?

No, the Poisson distribution is best suited for rare events that occur independently of each other. It is not appropriate for events that occur in a specific pattern or events that are dependent on each other.

5. How can the Poisson distribution be applied in real-world scenarios?

The Poisson distribution can be used in a variety of real-world scenarios, such as predicting the number of accidents on a highway, the number of calls received by a call center, or the number of customers in a shop. It is also commonly used in quality control and reliability analysis.

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