Theoretical DistributionsMCQPYQ Jan 21Question 3422 of 230
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A coin with probability for heads as 1/5\displaystyle 1/5 is tossed 100\displaystyle 100 times. The standard deviation of the number of head 5\displaystyle 5 turned up is.

Options

A3\displaystyle 3
B2\displaystyle 2
C4\displaystyle 4
D6\displaystyle 6
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Correct Answer

✅ Option c — 4\displaystyle 4

All Options:

  • A3\displaystyle 3
  • B2\displaystyle 2
  • C4\displaystyle 4
  • D6\displaystyle 6

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Detailed Solution & Explanation

**Standard Deviation of Number of Heads** **Given:** - n=100\displaystyle n = 100 tosses - p=P(head)=frac15\displaystyle p = P(\text{head}) = \\frac{1}{5} - q=1−p=1−frac15=frac45\displaystyle q = 1 - p = 1 - \\frac{1}{5} = \\frac{4}{5} **Step 1: Calculate the Variance** Variance=npq=100×frac15×frac45\text{Variance} = npq = 100 \times \\frac{1}{5} \times \\frac{4}{5} =100×frac425=frac40025=16= 100 \times \\frac{4}{25} = \\frac{400}{25} = 16 **Step 2: Calculate the Standard Deviation** SD=sqrtVariance=sqrt16=4\text{SD} = \\sqrt{\text{Variance}} = \\sqrt{16} = 4 **Checking the options:** - Option A: 3\displaystyle 3 ✗ - Option B: 2\displaystyle 2 ✗ - **Option C: 4\displaystyle 4** ✓ - Option D: 6\displaystyle 6 ✗ **Summary:** Mean=np=100×frac15=20\text{Mean} = np = 100 \times \\frac{1}{5} = 20 Variance=npq=100×frac15×frac45=16\text{Variance} = npq = 100 \times \\frac{1}{5} \times \\frac{4}{5} = 16 Standard Deviation=sqrt16=4\text{Standard Deviation} = \\sqrt{16} = 4 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.

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.

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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