$X$ is normally distributed with mean $4$ and variance $6$. Find the probability that $X$ takes a negative value.

(Round answer up to $4$ decimal places)

(Write answer up to $4$ decimal places)

If $T~\mathrm{N}\left(10, {\sigma }^2\right)$ and $\mathrm{P}\left(T>14.7\right)=0.04$, find the value of $\sigma$.

(Round answer up to $2$ decimal places)

It is given that $V~\mathrm{N}\left(\mu , 13\right)$ and $\mathrm{P}\left(V<15\right)=0.75$. Find the value of $\mu$.

(Round answer up to $1$ decimal places)

The variable $W~\mathrm{N}\left(\mu ,{\sigma }^2\right)$. Given that $\mu =4\sigma$ and $P(W<83)=0.95$, find the value of $\mu$ and of $\sigma$.

(Write final answer up to $1$ decimal place)

(Write final answer up to $1$ decimal place)

For the variable $V~\mathrm{N}\left(\mu ,{\sigma }^2\right)$, it is given that $P(V<8.4)=0.7509$ and $P(V>9.2)=0.1385$. Find the value of $\mu$ and of $\sigma$, and calculate $P(V⩽10)$.

(Round answer up to $2$ decimal places)

(Round answer up to $2$ decimal places)