import numpy as np
from scipy.stats import norm

np.set_printoptions(precision=2, suppress=True)

scores = norm(loc=70, scale=8)
lo, hi = scores.interval(0.90)
rng = np.random.default_rng(20260625)
sample = scores.rvs(size=5, random_state=rng)
q = np.array([0.1, 0.5, 0.9])

print(f"mean/std: {scores.mean():.1f} {scores.std():.1f}")
print(f"pdf(75): {scores.pdf(75):.4f}")
print(f"cdf(75): {scores.cdf(75):.4f}")
print(f"sf(85): {scores.sf(85):.4f}")
print(f"central 90%: {lo:.2f} to {hi:.2f}")
print(f"ppf(0.90): {scores.ppf(0.90):.2f}")
print("sample:", sample)
print("cdf(ppf(q)):", np.round(scores.cdf(scores.ppf(q)), 1))