Question

Assertion (A): If \(X\sim N(\mu,\sigma^{2})\), then \[ P(X<\mu)=0.5. \] Reason (R): Normal distribution is symmetric about its mean.

• A. Both A and R are true and R is the correct explanation of A.
• B. Both A and R are true but R is not the correct explanation of A.
• C. A is true but R is false.
• D. A is false but R is true.

Hint:

For a normal distribution: \[ \boxed{ P(X\mu)=\frac12. } \] Also remember the important empirical rule: \[ \begin{aligned} P(\mu-\sigma P(\mu-2\sigma P(\mu-3\sigma<X<\mu+3\sigma) &\approx 99.7\%. \end{aligned} \] Whenever an Assertion-Reason question involves the symmetry of the normal distribution, first recall that the mean divides the total probability into two equal halves.

Answer 1

The Correct Option is A