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

$\mathbb P(Z$

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

$\mathbb P(Z$
$\mathbb P(|Z|$

So

$\mathbb P(Z$

or about 99.9%.