Which of the following statements are true if $z$ is the standard normal variable?

Hint: Sketch a normal curve.

Select four $(4)$ true statements from the list below:

About $99\mathrm{.}7\%$ of the area under the normal curve lies between $z=-3$ and $z=3.$

If then $P(za)>0\mathrm{.}5$

If $a>b,$ then $P(za)-P(zb)$ cannot be positive.

$P(z-2)=1-P(z2)$

$P(z-2\mathrm{.}5)$ is larger than $P(z1\mathrm{.}5)$

$P(z1\mathrm{.}5)$ is twice $P(z0\mathrm{.}75)$

$P(z0)$ is larger than $P(z0)$

The standard normal distribution has a mean of $1$ and a variance of $0.$

If the means of two perfectly normal distributions are different, their medians could be equal.

The $z-$score corresponding to the $75$ th percentile is negative.