from random import normalvariate
from math import sqrt

def moyenne(L):
    s=0
    for k in L:
        s=s+k
    return s/len(L)

def ecart_type(L):
    e=0
    m=moyenne(L)
    for v in L:
        e=e+(v-m)**2
    return sqrt(e/len(L))

def simule_loi_normale(n,mu,sigma):
    L=[]
    for k in range(n):
        L.append(normalvariate(mu, sigma))
    return L

def serie_moyennes(N,n,mu,sigma):
    S=[]
    for k in range(N):
        L=simule_loi_normale(n,mu,sigma)
        S.append(moyenne(L))
    return S

def prop_int_ksigma(N,n,mu,sigma,k):
    e=0
    S=serie_moyennes(N,n,mu,sigma)
    for m in S:
        if abs(m-mu)<k*sigma/sqrt(n):
            e=e+1
    return e/N

def prop_int_ks(N,n,mu,sigma,k):
    e=0
    S=serie_moyennes(N,n,mu,sigma)
    s=ecart_type(S)
    for m in S:
        if abs(m-mu)<k*s:
            e=e+1
    return e/N