Question

A town planner is investigating pedestrian traffic congestion at the entries to a public space. One of the statistics recorded is the number of pedestrians using each entry (passing in or out) in each 15-minute period during a working day. If X is the number of pedestrians recorded in each 15-minute interval, would observations of X follow a binomial distribution? Justify your answer.

(please use descriptive language/detail and show working as I struggle with anything to do with statistical analysis and would like to learn, thankyou) ps. question is worth 3 marks so I assume a reasonable length answer is expected

Answer 1

No, X does not follows the binomial distribution.

One of the property of the binomial distribution is the total number of trials are fixed.

Here the trial result of the experiment is the pedestrian passing in or out in 15 minute of period.

but total number of trials ( pedestrians ) entry are not fixed.

Here X is the random variable which takes the number of pedestrians recorded in each 15 minute interval.

Therefore X takes values as 0, 1, 2, ....

And so X follows Poisson distribution and not binomial distribution.