CA Foundation · Quantitative Aptitude · Theoretical Distributions
Which of the following situations is best modelled by a Poisson distribution?
Cheques dishonoured per day at a bank branch is best modelled by a Poisson distribution, because it counts rare, independent events occurring at a constant average rate over a time interval, with no fixed number of trials. The other situations are binomial or normal.
- ANumber of heads in 10 tosses of a fair coin
- BNumber of cheques dishonoured per day at a bank branch, where such events are rare and occur independently at a constant average rateCorrect
- CHeights of students in a class
- DNumber of defective items in a sample of 5 drawn with a fixed defect probability
Explanation
The Poisson distribution counts rare, independent events occurring over a continuous interval of time or space at a constant average rate. Dishonoured cheques per day fit this. Coin tosses and fixed-size samples with a fixed probability are binomial, and heights are continuous, hence normal.
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.
More Theoretical Distributions questions
- The daily sales of a Jaipur sweet shop are normally distributed with mean ₹8,000 and standard deviation ₹1,000. Given P(0 < Z < 2) = 0.4772,…
- A discrete random variable X takes the values 1, 2, 3 and 4 with probabilities k, 2k, 3k and 4k respectively. What is the value of P(X ≥ 3)?
- A fair coin is tossed 4 times. What is the probability of getting exactly 2 heads?
- A random variable X follows a binomial distribution with n = 20 and p = 0.3. What is the variance of X?
- For a binomial distribution with n = 20 and p = 0.3, what are the mean and the variance respectively?
- The number of cheques returned unpaid at a Nashik bank branch per day follows a Poisson distribution with mean 2. Using e^-2 = 0.1353 and e^…