Function with For Loop by Row

Question

I am trying to achieve a monte carlo simulation by row (name) in this case, I am able to get the monte carlo simulations but the random normal distribution it is doing is consistent across all names when I am seeking for it to be independent and random by row. I have exhausted all my ideas and I am seeking help now :)

The result this results in is clearly 'row' specific meaning the rnd.gauss(mean, std) is consistent when I want it to truly be unique and random by row/name. I have tried adding a for loop utilizing 'name' but it is not working as expected.

import random as rnd
import pandas as pd

data = [['lj', 22.72, 37, 9.8], ['nc', 13.24, 30.9, 4.4],['bm', 13.77, 26.3, 9.3], ['jl', 12, 25.9, 7.2]]
df = pd.DataFrame(data, columns= ['Name', 'Proj', 'Ceil', 'Floor'])

mean = df['Proj'].astype(float)
std = ((df['Ceil'].astype(float) - df['Floor'].astype(float))/2).astype(float)
num_of_sims = 10
name = df['Name']

output = pd.DataFrame([])

def simulation (n):
    simulated_projection = 0
    simulated_projection = rnd.gauss(mean, std)
    return simulated_projection

for i in range(num_of_sims):
    projection = simulation(num_of_sims)
    output = output.append(projection, True)

	0	1	2	3
0	19.057055	9.671322	11.480660	9.481726
1	28.160946	18.540922	17.170591	15.740650
2	27.912110	18.298490	17.015069	15.569576
3	35.364650	25.559236	21.672906	20.693197
4	8.840950	-0.281869	5.095593	2.458153
5	27.978372	18.363047	17.056483	15.615131
6	47.647661	37.526140	29.349788	29.137767
7	12.740099	3.516935	7.532562	5.138818
8	20.443244	11.021837	12.347027	10.434730
9	33.104873	23.357615	20.260545	19.139600

The output is the table above, you can see that the rnd.gauss(mean, std) is creating the desired randomized normal distribution per each column however the randomization per row is consistent. For example row 3 shows 35 for column 0, column 1 is also a larger value 25, column 2 also a large value 21 etc. Row 4 show 8 for column 0, column 1 is also small -0.28, column 2 is also small 5 etc.

What I am looking for is the randomization to be independent by row (def simulation) to achieve a more randomized sampling per simulation.