How to calculate normal distribution probabilities in various languages

normalProbabilities.py

# http://docs.scipy.org/doc/scipy/reference/generated/scipy.stats.norm.html


import scipy.stats
Z = scipy.stats.norm(0, 1)

Z.pdf(0)
Z.cdf(0)

# mean of 5, standard deviation of 2
X = scipy.stats.norm(5, 2)
X.cdf(5)
X.cdf(0)

normalProbabilities.R

# dnorm gives the pdf for the normal at x
dnorm(1)
# pnorm gives the cdf for the normal at x
# P(Z < 1)
pnorm(1)

# They also accept parameters to specify the mean and standard deviation
# X ~ N(mean = 2, sd = 4)
# P(X < 1)
pnorm(1, 2, 4)

# If we have something like
# X ~ N(mean = 2, sd = 4)
# and want to find
# P(1 < X < 2)
# we can provide multiple arguments for x and take the difference
diff(pnorm(c(1,2), 2, 4))