Theoretical DistributionsMCQMTP May 18Question 3434 of 230
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The mean of Binomial distribution is 4\displaystyle 4 and the Standard Deviation sqrt3\displaystyle \\sqrt{3}, what is the value of p\displaystyle p.

Options

A1/3\displaystyle 1/3
B1/4\displaystyle 1/4
C1/5\displaystyle 1/5
D3/4\displaystyle 3/4
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Correct Answer

✅ Option d — 3/4\displaystyle 3/4

All Options:

  • A1/3\displaystyle 1/3
  • B1/4\displaystyle 1/4
  • C1/5\displaystyle 1/5
  • D3/4\displaystyle 3/4

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Detailed Solution & Explanation

**Binomial Distribution: Finding p from Mean and SD**\n\nGiven: Mean =np=4\displaystyle = np = 4, Standard Deviation =sqrt3\displaystyle = \\sqrt{3}\n\n**Step 1: Find the variance**\ntextVariance=(textSD)2=(sqrt3)2=3\\text{Variance} = (\\text{SD})^2 = (\\sqrt{3})^2 = 3\n\n**Step 2: Find q**\ntextVariance=npqRightarrowq=fractextVariancetextMean=frac34\\text{Variance} = npq \\Rightarrow q = \\frac{\\text{Variance}}{\\text{Mean}} = \\frac{3}{4}\n\n**Step 3: Find p**\np=1−q=1−frac34=frac14p = 1 - q = 1 - \\frac{3}{4} = \\frac{1}{4}\n\n**Step 4: Verify**\nn=fractextMeanp=frac41/4=16n = \\frac{\\text{Mean}}{p} = \\frac{4}{1/4} = 16\ntextVariance=npq=16timesfrac14timesfrac34=3checkmark\\text{Variance} = npq = 16 \\times \\frac{1}{4} \\times \\frac{3}{4} = 3 \\checkmark\n\n> **Note:** The correct value is p=frac14\displaystyle p = \\frac{1}{4} (Option B). The textbook answer key lists Option D (3/4\displaystyle 3/4), which is actually the value of q\displaystyle q, not p\displaystyle p.\n\nHence, **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.

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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