Question

1. A grocery store counts the number of customers who arrive during an hour. The average over a year is 29 customers per hour. Assume the arrival of customers follows a Poisson distribution. (It usually does.) Find the probability that at least one customer arrives in a particular one minute period. Round your answer to 3 decimals. Find the probability that at least two customers arrive in a particular 2 minute period.

2. Label each as one of the following

Exponential

Poisson

Binomial

Uniform

1. a constant probability density and charts as a rectangle
2. fixed number of trials with only 2 possible outcomes and the trials are independent  
3. models the time until some specifi event occurs such as equipment failure  
4. events happen with a known average rate and independently of the time since the last event  

Answer 1

1:

Average number of customers per hour that is in 60 minutes is 29. Let X is a random variable shows the number of person arrive in a one minute interval. Here X has Poisson distribution with parameter

The probability that at least one customer arrives in a particular one minute period is

Answer: 0.3833

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Let X is a random variable shows the number of customers arrive in a 2 minutes interval. Here X has Poisson distribution with parameter

The probability that at least 2 customer arrives in a particular 2 minutes period is

Answer: 0.2520

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1. a constant probability density and charts as a rectangle : Uniform
2. fixed number of trials with only 2 possible outcomes and the trials are independent : Binomial
3. models the time until some specific event occurs such as equipment failure : Exponential
4. events happen with a known average rate and independently of the time since the last event : Poisson