I am new to the normal distribution topic. While I have understood and solved various different kind of questions, the normal distribution questions with absolute value, are the ones I have no idea on. So could someone plz help me in these type of questions? Here are the ones I am stuck at. (Thanks a LOT in advance for your help)
If $Z$ is the coefficient of normally distributed random variable, find ‘$a$’ such that: $\mathbb P(|Z| < a) = 0.383$
$X$ is a normally distributed random variable with mean($\mu$) $84$ and variance($\sigma^2$) $12$, calculate: $\mathbb P(|X-84| > 2.9)$
If $X$ is normally distributed with mean($\mu$) $400$ and standard deviation($\sigma$) $8$, find the value of $k$ such that: $\mathbb P(|X-400| < k) = 0.975$
$X$ is normally distributed random variable with mean $m$ and standard deviation $s$ . Find the value of $m$ and the value of $s$ if: $\mathbb P (X<35) = 0.02$ & $\mathbb P(35 < X < 45) = 0.65$. (for this, I just need help in the second part with the two values case. The first part Ive done already)