def normal_lower_bound(probability, mu=0, sigma=1):
"""returns the z for which P(>= z) = probability"""
return inverse_normal_cdf(1 - probability, mu, sigma)
def normal_upper_bound(probability, mu=0, sigma=1):
"""returns the z for which P(Z <= z) = probablity"""
return inverse_normal_cdf(probability, mu, sigma)