import statistics

mean = 20
sd = 2

x1 = 19.5
x2_a = 20
x2_b = 22

nd = statistics.NormalDist(mean, sd)

print(round(nd.cdf(x1), 3))
print(round(nd.cdf(x2_b)-nd.cdf(x2_a), 3))

import math as m

def ND(x,mean,sd):
z = (x-mean)/(2*m.sqrt(2))
cdf = 0.5*(1 + m.erf(z))
return cdf 

print(f"{ND(19.5,20,2):.4f}")
p1 = ND(20,20,2)
p2 = ND(22,20,2)
print(f"{p2-p1:.4f}")

import math

mu = 20
sigma = 2

x_1 = 19.5 

x_2_a = 20
x_2_b = 22

# P(X <= x) = 0.5 * (1+math.erf((x - mu)/(sigma * 2**0.5)))
p_less_than_19_5 = 0.5 * (1+math.erf((x_1 - mu)/(sigma * 2**0.5)))

print(round(p_less_than_19_5,3))

# (a <= X <= b) = F(b) - F(a)
p_between_20_and_22 = 0.5 * (1+math.erf((x_2_b - mu)/(sigma * 2**0.5))) - 0.5 * (1+math.erf((x_2_a - mu)/(sigma * 2**0.5)))

print(round(p_between_20_and_22, 3))

stdin <- file('stdin')
open(stdin)

stats <- as.numeric(strsplit(trimws(readLines(stdin, n = 1, warn = FALSE), which = "right"), " ")[[1]])
less <- as.numeric(trimws(readLines(stdin, n = 1, warn = FALSE), which = "both"))
between <- as.numeric(strsplit(trimws(readLines(stdin, n = 1, warn = FALSE), which = "right"), " ")[[1]])
mean <- stats[1]
sd <- stats[2]
cat(round(1 - pnorm(less, mean, sd, FALSE),3), fill=TRUE)
cat(round(pnorm(between[2], mean, sd, TRUE) - pnorm(between[1], mean, sd, TRUE),3), fill=TRUE)

import math as m
def cdf(mn, std, x):
    return 0.5 * (1 + m.erf((x-mn)/(std*m.sqrt(2))))
    
print(f'{cdf(20,2,19.5):.3f}')
print(f'{cdf(20,2,22) - cdf(20,2,20):.3f}')