Theoretical DistributionsMTP Dec 22 - Series IIQuestion 3989 of 230
All Questions

For a normal distribution, the first and third quartile are given to be 37 and 49, the mode of the distribution is.

Options

A37
B49
C43
D45
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Correct Answer

✅ Option c — 43

All Options:

  • A37
  • B49
  • C43
  • D45

Detailed Solution & Explanation

**Mode of a Normal Distribution from Quartiles** In a normal distribution, the probability density curve is perfectly symmetrical. Due to this symmetry, the mean, median, and mode coincide at the exact center of the distribution. The median (which equals the mode) is located exactly midway between the first quartile (Q1\displaystyle Q_1) and the third quartile (Q3\displaystyle Q_3): textMode=textMedian=fracQ1+Q32\\text{Mode} = \\text{Median} = \\frac{Q_1 + Q_3}{2} **Given values:** - First Quartile (Q1\displaystyle Q_1) = 37\displaystyle 37 - Third Quartile (Q3\displaystyle Q_3) = 49\displaystyle 49 **Calculation:** textMode=frac37+492=frac862=43\\text{Mode} = \\frac{37 + 49}{2} = \\frac{86}{2} = 43 Thus, the mode of the normal distribution is 43\displaystyle 43, which corresponds to Option C. 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.

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