The random variable $Z$ is normally distributed with mean $0$ and variance $1$. Find the following probability, correct to $3$ significant figures.

$P(-1.777<Z<-0.746)$

The random variable $Z$ is normally distributed with mean $0$ and variance $1$. Find the following probability, correct to $3$ significant figures.

$P(-1.008<Z<-0.337)$

The random variable $Z$ is normally distributed with mean $0$ and variance $1$. Find the following probability, correct to $3$ significant figures.

$P(-1.2<Z<1.2)$

The random variable $Z$ is normally distributed with mean $0$ and variance $1$. Find the following probability, correct to $3$ significant figures.

$P(-1.667<Z<2.667)$

The random variable $Z$ is normally distributed with mean $0$ and variance $1$. Find the following probability, correct to $3$ significant figures.

$P\left(-\frac{3}{4}⩽Z<\frac{8}{5}\right)$

The random variable $Z$ is normally distributed with mean $0$ and variance $1$. Find the following probability, correct to $3$ significant figures.

$P\left(\sqrt{2}⩽Z<\sqrt{5}\right)$

Given that $Z~\mathrm{N}(0,1),$ find the value of $k,$ given that:

$P(Z<k)=0.9087$

Given that $Z~\mathrm{N}(0,1),$ find the value of $k,$ given that:

$P(Z<k)=0.5442$

Given that $Z~\mathrm{N}(0,1),$ find the value of $k,$ given that:

$P(Z>k)=0.2743$