Finding the area under a bell curve

Questions
1

I’m following a video tutorial on how to use Z-scores to answer the question
“What is the probability an observation is greater/less than some value x”

At the point in the video linked, the author uses a look-up table instead of a calculation to determine the area under the bell curve.

Is there a function in Mathematica to calculate the area without use of a look-up table?

Open in Wolfram Cloud ↗
2

Here is a way:

Probability[x > 8,
 Distributed[x,
  NormalDistribution[75/10, 25/1000]]]
N[%, 5]
3

Gianluca,

On 12.3.1 I get

Internal precision limit $MaxExtraPrecision = 50.` reached while
evaluating 1/2 (1-Erf[10\ Sqrt[2]])

Block[{$MaxExtraPrecision = 100}, 
 Probability[x > 8, Distributed[x, NormalDistribution[75/10, 25/1000]]] // N[#, 5] &]
(* 2.7536*10^-89 *)

Or without rationalizing

Probability[x > 8, Distributed[x, NormalDistribution[mean, standardDeviation]]]
(* 2.75362*10^-89 *)