Theoretical DistributionsPYQ Jan 26Question 4292 of 230
All Questions

For a binomial distribution, if the mean is 10 and the standard deviation is 3, find n. (number of trials)

Options

A30
B90
C15
D100
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Correct Answer

✅ Option d — 100

All Options:

  • A30
  • B90
  • C15
  • D100

Detailed Solution & Explanation

For a binomial distribution, the formulas for the mean and standard deviation are: Mean=np\text{Mean} = np Standard Deviation=npq\text{Standard Deviation} = \sqrt{npq} where: - n\displaystyle n is the number of trials - p\displaystyle p is the probability of success - q=1−p\displaystyle q = 1 - p is the probability of failure
We are given: - Mean=np=10— (1)\displaystyle \text{Mean} = np = 10 \quad \text{--- (1)} - Standard Deviation=npq=3\displaystyle \text{Standard Deviation} = \sqrt{npq} = 3 Squaring the standard deviation gives the variance: Variance=npq=32=9— (2)\text{Variance} = npq = 3^2 = 9 \quad \text{--- (2)}
Dividing equation (2) by equation (1): npqnp=910  ⟹  q=0.9\frac{npq}{np} = \frac{9}{10} \implies q = 0.9
Since p+q=1\displaystyle p + q = 1, we can find p\displaystyle p: p=1−q=1−0.9=0.1p = 1 - q = 1 - 0.9 = 0.1
Now we substitute p=0.1\displaystyle p = 0.1 back into equation (1) to solve for n\displaystyle n: n(0.1)=10n(0.1) = 10 n=100.1=100n = \frac{10}{0.1} = 100 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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