Distribution of outcomes in dice experiments

So I wrote a short Python function to plot distribution outcome of dice experiments. It's working fine but when I run for example dice(1,5000) or dice(10,5000) or dice(100,5000) the histograms shows a skewed distribution (high preference for 6). However, the average shows the to-be expected value of around 3.5. I thought maybe this has sth to do with the random number generation so I tried out 2 methods: 1st with random.randint and the 2nd one is as in code. However, they deliver similar results. Like there is something wrong with the upper limit. But I'm not sure why there is such a skewed distribution.

import matplotlib.pyplot as plt
import numpy as np
import random

# Throw a dice
def dice(N,n):
    result = np.zeros((n,N))
    '''
    N: number of dices
    n: number of experiment
    '''
    for i in range(n):
        for j in range(N):
            random_number = random.random()
            outcome = int(random_number * 6 + 1)
            result[i][j]=outcome
    laverage = np.mean(result)

    print('Result of throwing %d dice(s) for %d times:'%(N,n),result)
    print(laverage)
    plt.hist(np.resize(result,(N*n,1)),bins=[x for x in range(1,7)])
    plt.xlabel('Outcome')
    plt.ylabel('Number of occurences')
    plt.show()

dice(1,5000)