Question

find the probability that a data value picked at random from a normally distributed population will have a standard score that corresponds to the following Less than 3.00

Answer 1

$\mathbb P(Z<3)=\mathbb P(Z<-3)+\mathbb P(|Z|<3)$

The empirical rule says that approximately 99.7% of any normal distributions falls within three standard deviations of the mean, which leaves 0.3% outside that range, and due to the distribution's symmetry, 0.15% to either side. This means

$\mathbb P(Z<-3)=0.0015$
$\mathbb P(|Z|<3)=0.997$

So

$\mathbb P(Z<3)\approx0.0015+0.997=0.9985$

or about 99.9%.