CUET Mathematics 2025 30 May Shift 2 PYQs

Let $F(z)$ be the cumulative density function of the standard normal variate $z$, then which of the following are correct?

(A) $F(z) = \frac{1}{\sqrt{2\pi}} \int_{-\infty}^z e^{-\frac{t^2}{2}} dt$, $-\infty < z < \infty$

(B) $F(-z) = 1 - F(z)$

(C) $F(0) = 0$

(D) $F(\infty) = 1$

Choose the correct answer from the options given below:

If $X$ is a normal variate with mean 12 and standard deviation 4, then $P[X \ge 20]$ is:

[Given that: $P[0 \le Z \le z] = 0.4772]$

The curve $y = f(x)$ is normal probability curve, then which of the following statements are correct?

(A) mean, median and mode of the distribution coincide.

(B) the area bounded by the curve $y = f(x)$ and $x$-axis is one unit.

(C) The curve is symmetrical about the line $x = \mu$, where $\mu$ is the mean.

(D) $y$-axis is an asymptote to the curve.

Choose the correct answer from the options given below: