Skip to content

CA Foundation · Quantitative Aptitude · Theoretical Distributions

A bank in Chennai records the number of customers arriving at a counter in a 10-minute interval. Arrivals are rare, random and independent, and the sample mean number of arrivals is 4. Which theoretical distribution is the most appropriate model?

The Poisson distribution with mean 4 is appropriate, because the variable counts rare, random and independent arrivals in a fixed interval and only the average rate is known. No fixed number of trials exists, so a binomial does not fit, and the count is discrete.

  1. ABinomial distribution with n = 4
  2. BPoisson distribution with mean 4Correct
  3. CNormal distribution with mean 4 and variance 16
  4. DUniform distribution between 0 and 4

Explanation

Counts of rare, random, independent events in a fixed interval, with only an average rate known, are modelled by a Poisson distribution. The parameter is the mean, so m = 4. A binomial needs a fixed number of trials with a success probability, which is not given. A normal model is for continuous data and the variance 16 would contradict the Poisson property that variance equals mean.

Did you get it right without looking?

One question tells you little. A timed set on Theoretical Distributions shows your real accuracy, how long you take and where you lose marks.

Practise Theoretical DistributionsFree diagnostic mock

More Theoretical Distributions questions