import math

def cdf(x, mu, sigma):
    return 0.5 + math.erf((x-mu)/(sigma*2**0.5))*0.5

n_samples=100
lower_bound = 490
upper_bound  =510
population_mu = 500
population_sigma = 80

sample_mean_mu=population_mu
sample_mean_sigma=population_sigma/n_samples**0.5

Prob_l = cdf(lower_bound, sample_mean_mu, sample_mean_sigma)
Prob_u = cdf(upper_bound, sample_mean_mu, sample_mean_sigma)

print('{:0.4f}'.format(Prob_u-Prob_l))