If 'x' and 'y' are independent normal variate with mean and SD $\mu_1, \mu_2$ and $\sigma_1, \sigma_2$ respectively, then for $z = x + y$ which also follows normal distribution mean and SD are:

Mean $= \mu_1 + \mu_2$, SD $= \sqrt{\sigma_1^2 + \sigma_2^2}$

Mean $=$ $(\mu_1 + \mu_2) / 2$, SD $= \sqrt{\sigma_1^2 + \sigma_2^2}$

Mean $= \mu_1 - \mu_2$, SD $= \sqrt{\sigma_1^2 + \sigma_2^2}$

Mean $= (\mu_1 - \mu_2) / 2$, SD $= \sqrt{\sigma_1^2 + \sigma_2^2}$

The correct answer is Option a: Mean $= \mu_1 + \mu_2$, SD $= \sqrt{\sigma_1^2 + \sigma_2^2}$. PYQ Dec 23

Theoretical DistributionsPYQ Dec 23Question 3555 of 221

If 'x' and 'y' are independent normal variate with mean and SD $\displaystyle \mu_1, \mu_2$ and $\displaystyle \sigma_1, \sigma_2$ respectively, then for $\displaystyle z = x + y$ which also follows normal distribution mean and SD are:

AMean

\displaystyle = \mu_1 + \mu_2

, SD

\displaystyle = \sqrt{\sigma_1^2 + \sigma_2^2}

BMean

\displaystyle =

\displaystyle (\mu_1 + \mu_2) / 2

, SD

\displaystyle = \sqrt{\sigma_1^2 + \sigma_2^2}

CMean

\displaystyle = \mu_1 - \mu_2

, SD

\displaystyle = \sqrt{\sigma_1^2 + \sigma_2^2}

DMean

\displaystyle = (\mu_1 - \mu_2) / 2

, SD

\displaystyle = \sqrt{\sigma_1^2 + \sigma_2^2}

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✅ Option a — Mean $\displaystyle = \mu_1 + \mu_2$ , SD $\displaystyle = \sqrt{\sigma_1^2 + \sigma_2^2}$

AMean $\displaystyle = \mu_1 + \mu_2$ , SD $\displaystyle = \sqrt{\sigma_1^2 + \sigma_2^2}$
BMean $\displaystyle =$ $\displaystyle (\mu_1 + \mu_2) / 2$ , SD $\displaystyle = \sqrt{\sigma_1^2 + \sigma_2^2}$
CMean $\displaystyle = \mu_1 - \mu_2$ , SD $\displaystyle = \sqrt{\sigma_1^2 + \sigma_2^2}$
DMean $\displaystyle = (\mu_1 - \mu_2) / 2$ , SD $\displaystyle = \sqrt{\sigma_1^2 + \sigma_2^2}$

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.

Exam Strategy Tip

This topic carries 4-6 Marks weightage. Focus on understanding core concepts rather than memorizing.

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