PDF, probability, variance, statis

Question

Let X be normal with mean 1 and variance 4. LetY =2X+3.

Find P(Y ≥ 0)

I've solved E(Y) = 5 and Var(Y)=16. How do I apply this solve $P(Y\geq 0)$

Answer 1

now you can standardize the variable: $P(Y\leq 0)=\Phi \left( \frac{0-\mu}{\sigma} \right)$, where $\Phi(.)$ is the function of the standard normal distribution. Here you have to take the complementary possibility $P(Y\geq 0)=1-\Phi \left( \frac{0-\mu}{\sigma} \right)$

greetings,

calculus