Theoretical DistributionsMCQMTP Dec 22 Series IQuestion 3459 of 230
All Questions

Examine the validity of the following: Mean and standard deviation of a binomial distribution are 10 and 4 respective:

Options

ANot Valid
BValid
CBoth A and B
DNeither A nor B
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Correct Answer

✅ Option a — Not Valid

All Options:

  • ANot Valid
  • BValid
  • CBoth A and B
  • DNeither A nor B

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Detailed Solution & Explanation

Given: Mean =np=10\displaystyle = np = 10 and Standard Deviation =4\displaystyle = 4, so Variance =npq=16\displaystyle = np q = 16. To check validity, we compute q\displaystyle q: q=VarianceMean=npqnp=1610=1.6q = \frac{\text{Variance}}{\text{Mean}} = \frac{npq}{np} = \frac{16}{10} = 1.6 Since q=1.6>1\displaystyle q = 1.6 > 1, this is **impossible** because q\displaystyle q (probability) must satisfy 0≤q≤1\displaystyle 0 \leq q \leq 1. Also, p=1−q=1−1.6=−0.6<0\displaystyle p = 1 - q = 1 - 1.6 = -0.6 < 0, which is also impossible for a probability. **Note**: In a valid binomial distribution, Variance <\displaystyle < Mean (since q<1\displaystyle q < 1), i.e., npq<np\displaystyle npq < np. Here Variance =16>\displaystyle = 16 > Mean =10\displaystyle = 10, which violates this condition. Therefore, the given parameters are **Not Valid**. Hence, **Option A** 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

Standard Deviation

A measure of the dispersion or spread of values in a data set around the mean. It is the square root of Variance. A lower standard deviation indicates data points are clustered close to the mean; a higher value indicates greater spread.

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,

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