# Let us use Python to flip a coin.
import random

coin = random.choice(['Heads', 'Tails'])
print('Coin flip result:', coin)

# Let us repeat the coin flip many times to see the probability in action.
flips = 100
heads_count = 0
for i in range(flips):
    if random.choice(['Heads', 'Tails']) == 'Heads':
        heads_count += 1
prob_heads = heads_count / flips
print('Proportion of heads:', prob_heads)

# Let us make some random numbers that follow a normal distribution.
import numpy as np

numbers = np.random.normal(loc=0, scale=1, size=1000)
print('First 10 numbers:', numbers[:10])

# Let us see what shape our numbers make.
import matplotlib.pyplot as plt

plt.hist(numbers, bins=30, color='skyblue')
plt.title('Histogram of Normally Distributed Numbers')
plt.xlabel('Value')
plt.ylabel('Frequency')
plt.show()

# What do mean and standard deviation mean?
mean = np.mean(numbers)
std = np.std(numbers)
print('Mean:', mean)
print('Standard deviation:', std)

# How likely is a number in our group to be close to zero?
close_count = sum(abs(x) < 1 for x in numbers)
prob_close = close_count / len(numbers)
print('Fraction between -1 and 1:', prob_close)

# Let the user try picking their own mean and standard deviation.
user_mean = float(input('Pick a mean (try 5): '))
user_std = float(input('Pick a standard deviation (try 2): '))
user_numbers = np.random.normal(loc=user_mean, scale=user_std, size=1000)
plt.hist(user_numbers, bins=30, color='lightgreen')
plt.title('Your Normal Distribution')
plt.xlabel('Value')
plt.ylabel('Frequency')
plt.show()

# Let us calculate the probability that a number is greater than 7 in your data.
count_above_7 = sum(x > 7 for x in user_numbers)
prob_above_7 = count_above_7 / len(user_numbers)
print('Fraction above 7:', prob_above_7)

# What if we want to know about two conditions at once?
between_count = sum(3 < x < 7 for x in user_numbers)
prob_between = between_count / len(user_numbers)
print('Fraction between 3 and 7:', prob_between)

# Here is some pretend height data (in centimeters).
heights = [172, 160, 168, 174, 181, 165, 177, 170, 169, 173, 175, 162, 180]
plt.hist(heights, bins=5, color='plum')
plt.title('Histogram of Heights')
plt.xlabel('Height (cm)')
plt.ylabel('Number of People')
plt.show()

# Let us check mean and standard deviation of the heights.
height_mean = np.mean(heights)
height_std = np.std(heights)
print('Mean height:', height_mean)
print('Standard deviation:', height_std)

# Let us standardize the heights (z-scores).
z_scores = [(h - height_mean) / height_std for h in heights]
print('Z-scores:', z_scores)

# Let us sort the heights to see the range.
sorted_heights = sorted(heights)
print('Sorted heights:', sorted_heights)

# Let us combine two groups of heights and see how statistics change.
more_heights = [178, 166, 164, 171]
combined_heights = heights + more_heights
combined_mean = np.mean(combined_heights)
print('New mean:', combined_mean)

# Make 200 random test scores and count high scores.
scores = np.random.normal(loc=70, scale=10, size=200)
num_high = sum(s > 85 for s in scores)
print('Scores above 85:', num_high)

# What is the highest and lowest score in this class?
highest = np.max(scores)
lowest = np.min(scores)
print('Highest:', highest)
print('Lowest:', lowest)

# Let us draw the score distribution for the class.
plt.hist(scores, bins=20, color='salmon')
plt.title('Class Test Scores')
plt.xlabel('Score')
plt.ylabel('Number of Students')
plt.show()

# Final challenge: Ask the user to simulate their own test results.
user_avg = float(input('Pick a class mean (try 75): '))
user_sd = float(input('Pick a class standard deviation (try 12): '))
how_many = int(input('How many students? (try 40): '))
test_results = np.random.normal(user_avg, user_sd, how_many)
plt.hist(test_results, bins=10, color='orange')
plt.title('Your Simulated Test Results')
plt.xlabel('Score')
plt.ylabel('Number of Students')
plt.show()
print('Mean:', np.mean(test_results))
print('Standard deviation:', np.std(test_results))