Let \( f(x)=\frac{1}{\sqrt{2 \pi}} e^{-\frac{x^{2}}{2}} \) for \( x \in \mathbb{R} . \) Prove that \( f(x) \) is a probability density, i.e., show that \( \int_{-\infty}^{\infty} f(x)=1 \) Let \( X \) be a normal random variable with mean μ=10 and variance σ 2
=24. Compute (a) P(X>5) and (b) P(4 =4. Find the value of c such that P(X>c)=0.3