/* 

  Are under normal curve in Picat.

  From http://www.statistics101.net/statistics101web_000007.htm
  """
  From CliffsQuickReview Statistics, p. 56, example 2 
  A normal distribution of retail store purchases has 
  a mean of $14.31 and a standard deviation of 6.40. 
  What percentage of purchases were under $10? 
  """

  Exact value is:
  Picat> X=normal_dist_cdf(14.31,6.40,10)
  X = 0.250334499087507

  Cf my Gamble model gamble_area_under_normal_curve.rkt

  This program was created by Hakan Kjellerstrand, hakank@gmail.com
  See also my Picat page: http://www.hakank.org/picat/

*/

import ppl_distributions, ppl_utils.
import util.

main => go.

/*

  var : d
  Probabilities (truncated):
  39.185020727011505: 0.0001000000000000
  36.824144282241015: 0.0001000000000000
  36.638245205507623: 0.0001000000000000
  36.582206201483082: 0.0001000000000000
  .........
  -7.689877147364927: 0.0001000000000000
  -8.074843170614232: 0.0001000000000000
  -9.534611677397267: 0.0001000000000000
  -11.744059531790414: 0.0001000000000000
  mean = 14.2791

  var : p
  Probabilities:
  false: 0.7472000000000000
  true: 0.2528000000000000
  mean = [false = 0.7472,true = 0.2528]

*/
go ?=>
  reset_store,
  run_model(10_000,$model,[show_probs_trunc,mean]),
  nl,
  % show_store_lengths,nl,
  % fail,
  nl.
go => true.
  
  
model() =>
  D = normal_dist(14.31,6.40),
  P = check(D < 10),
  
  add("d",D),
  add("p",P).