014. Day 6 - The Central Limit Theorem I.py

# Problem: https://www.hackerrank.com/challenges/s10-the-central-limit-theorem-1/problem
# Score: 30


import math


def cdf(x, mean, std):
    return 1/2*(1+math.erf((x-mean) / std / 2**(1/2)))


# inputs
mean = 205
std = 15
n = 49
target = 9800

# characteristics of sum
mean_s = n * mean
std_s = std * n**(1/2)

# Find the probability that sum <= 9800
print(round(cdf(target, mean_s, std_s), 4))