Theoretical DistributionsPYQ May 25Question 4086 of 230
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Poisson probability distribution is appropriately applied in

Options

AThe height of students in the university.
BThe distribution of passing of students in university examinations.
CTossing of a coin hundred times.
DNumber of deaths by a rare disease.
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Correct Answer

✅ Option d — Number of deaths by a rare disease.

All Options:

  • AThe height of students in the university.
  • BThe distribution of passing of students in university examinations.
  • CTossing of a coin hundred times.
  • DNumber of deaths by a rare disease.

Detailed Solution & Explanation

Let us examine the characteristics of the Poisson distribution:
1. The **Poisson distribution** is a discrete probability distribution that expresses the probability of a given number of events occurring in a fixed interval of time or space.
2. It is applied to events that are **rare** (where the probability of occurrence p\displaystyle p is very small, and the number of trials n\displaystyle n is very large, such that np=λ\displaystyle np = \lambda is a constant finite mean).
3. Let us evaluate the options:
- **Option a**: Height of students follows a continuous Normal distribution.
- **Option b**: Passing of students follows a Binomial distribution (constant probability of success).
- **Option c**: Tossing a coin follows a Binomial distribution (probability of success is 0.5\displaystyle 0.5, which is not small).
- **Option d**: The number of deaths by a rare disease represents a classic rare event with very small probability p\displaystyle p, making the Poisson distribution the appropriate choice.

Hence, **Option D** is the correct answer.

About This Chapter: Theoretical Distributions

Paper

Paper 3: Quantitative Aptitude

Weightage

4-6 Marks

Key Topics

Binomial, Poisson, Normal Distribution

This chapter covers Binomial, Poisson, Normal Distribution and is part of Paper 3: Quantitative Aptitude in the CA Foundation exam.

View Official ICAI Syllabus

Exam Strategy Tip

This topic carries 4-6 Marks weightage. Focus on understanding core concepts rather than memorizing.

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A random variable X\displaystyle X follows Binomial Distribution With E(x)=2\displaystyle E(x)=2 and V(x)=1.2\displaystyle V(x)=1.2, then the value of n\displaystyle n is

When 'p\displaystyle p' is large than 0.5\displaystyle 0.5, the Binomial Distribution is:

For a Poisson distribution,

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