Theoretical DistributionsMTP June 2023 Series IIQuestion 3976 of 230
All Questions

To find the distribution of number of airplanes crashing every hour in the world, which of the following distribution is appropriate to apply:

Options

ANormal distribution
BBinomial distribution
CPoisson distribution
DUsing any of the above will yield the same output
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Correct Answer

✅ Option c — Poisson distribution

All Options:

  • ANormal distribution
  • BBinomial distribution
  • CPoisson distribution
  • DUsing any of the above will yield the same output

Detailed Solution & Explanation

**Appropriate Probability Distribution for Airplane Crashes** **Step 1: Analyze the characteristics of the event** - An airplane crash is a rare event. - The total number of flights operating in the world per hour (n\displaystyle n) is extremely large. - The probability that any single flight crashes (p\displaystyle p) is extremely small. **Step 2: Compare probability distribution models** - **Binomial Distribution:** Used for a fixed number of independent trials with a constant probability of success. However, when n\displaystyle n is very large and p\displaystyle p is very small, calculating binomial coefficients becomes computationally impractical. - **Normal Distribution:** Used for continuous random variables and is symmetric. It is not suitable for counting rare, discrete events. - **Poisson Distribution:** This is a limiting case of the Binomial distribution when the number of trials n\displaystyle n is very large (ntoinfty\displaystyle n \\to \\infty) and the probability of success p\displaystyle p is very small (pto0\displaystyle p \\to 0), such that the product np=m\displaystyle np = m remains a constant, finite value. **Conclusion:** Since airplane crashes are rare discrete events occurring in a large population over a fixed interval of time, the **Poisson distribution** is the most appropriate model to apply. This corresponds to Option C. Hence, **Option C** 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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