from math import erf
n = 100
# map mean and sigma to normal distribution with
# the following parameters by The Centeral Limit Theorem
mean = n*500
sigma = n**0.5*80
# Defining Phi function for CDF of our 
# retrieved Normal Distribution 
phi = lambda x: 0.5*(1+erf((x-mean)/(2**0.5*sigma)))
target = 0.95  # initiating target of 95 %
# Probability of our confidance interval
# given z-score value
ci_prob = lambda z: phi(z*sigma+mean)-phi(-z*sigma+mean)
# True if our CI of z-score achieved desired probability
found = lambda z: target <= round(ci_prob(z), 3)
z = 0.01  # initial z-score
# interating z until our CI satisfies our target
while not found(z): z += 0.01 
# getting left and right interval values and mapping
# back from normal distribution to initial distribution 
# by multiplying both values by 1/n, i.e. values in
# initial distribution where n times less due to additive
# property of an EV
print(round((-z*sigma+mean)/n, 2))
print(round((z*sigma+mean)/n, 2))