Theoretical DistributionsMCQMTP Dec 2023 Series IIQuestion 3604 of 230
All Questions

Which of the following is not a characteristic of a normal probability distribution?

Options

AMean of the normally distributed population lies at the centre of its normal curve.
BIt is multi-modal
CThe mean, median and mode are equal
DIt is a symmetric curve.
For any discrepancies in this question, email contact@cadada.in

Correct Answer

✅ Option b — It is multi-modal

All Options:

  • AMean of the normally distributed population lies at the centre of its normal curve.
  • BIt is multi-modal
  • CThe mean, median and mode are equal
  • DIt is a symmetric curve.

Ad

Detailed Solution & Explanation

**Characteristics of a Normal Distribution**\n\nA normal distribution curve (or Gaussian curve) possesses the following fundamental properties:\n\n1. **Bell-Shaped and Continuous:** The curve is bell-shaped and continuous over the range (−infty,infty)\displaystyle (-\\infty, \\infty).\n2. **Symmetry:** It is perfectly symmetrical about the line x=mu\displaystyle x = \\mu. The area to the left of the mean is 0.5\displaystyle 0.5, and the area to the right is 0.5\displaystyle 0.5.\n3. **Equivalence of Central Tendencies:** Due to symmetry, the mean, median, and mode coincide at the center of the distribution:\n textMean=textMedian=textMode=mu\\text{Mean} = \\text{Median} = \\text{Mode} = \\mu\n4. **Uni-modal:** The curve has only one peak, which occurs at the mean x=mu\displaystyle x = \\mu. Thus, it is **uni-modal** (having a single mode), not multi-modal.\n5. **Asymptotic to the Base Line:** The tails of the curve asymptotically approach the horizontal axis but never touch it.\n\n**Evaluating the Options:**\n- **Option A:** "Mean of the normally distributed population lies at the centre of its normal curve." — This is a **true** characteristic.\n- **Option B:** "It is multi-modal" — This is **false** (it is uni-modal). Therefore, this is not a characteristic.\n- **Option C:** "The mean, median and mode are equal" — This is a **true** characteristic.\n- **Option D:** "It is a symmetric curve." — This is a **true** characteristic.\n\nHence, **Option B** 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.

Key Concepts to Understand

Probability

A numerical measure of the likelihood of an event occurring, expressed as a number between 0 (impossible) and 1 (certain). Formula: P(A) = Number of favorable outcomes / Total number of equally likely outcomes.

More Questions from Theoretical Distributions

Find the variance of binomial distribution with n=10\displaystyle n=10, p=0.3\displaystyle p=0.3

When p=0.5\displaystyle p=0.5, the binomial distribution is

If mean and standard deviation of a binomial distribution is 10\displaystyle 10 and 2\displaystyle 2 respectively, q\displaystyle q will be

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,

Ready to Master Theoretical Distributions?

Practice all 230 questions with instant feedback, earn XP, track your streaks, and ace your CA Foundation exam.

Start Practicing — It's Free