# FAST SUMMARY - Sports Analytics and Data Science - Desconhecido

Here is a summary of how the normal distribution can be used to approximate the binomial distribution:

The binomial distribution models the probability of k successes out of n trials, where each trial has a success probability p.

For large n and intermediate values of p (not too close to 0 or 1), the binomial distribution can be approximated by a normal distribution.

The mean of the normal approximation is np (the expected number of successes)

The standard deviation of the normal approximation is √(np(1−p))

This normal approximation works well when np > 10 and n(1-p) > 10

With this normal model, probabilities can be calculated using the 68-95-99.7 rule instead of binomial formulas

For example, if n=1000, p=0.4, the normal approximation mean is 1000(0.4) = 400. The approx standard deviation is √(1000(0.4)(0.6)) = 20.

So about 68% of outcomes are expected between 380 and 420 successes.

In summary, the normal distribution can provide a simpler probabilistic model that approximates the binomial in many practical use cases involving large samples. But the approximation may not hold for small n or p near 0 or 1.

Here is a summary of key points on using quantitative techniques for pricing analytics:

Statistical analysis of past sales data can reveal how demand responds to price changes (price elasticity of demand) for a product. This indicates optimal pricing levels.

Conjoint analysis surveys collect consumer preferences on various product attributes including price. This reveals willingness-to-pay and optimal price positioning.

Multivariate regression modeling can identify key factors influencing demand and price sensitivity like product features, brand, promotions, etc. This enables pricing optimization.

Data mining techniques like clustering and market basket analysis identify customer segments with distinct price sensitivities allowing customized pricing.

Time series forecasting and predictive analytics enable dynamic pricing by forecasting demand at various price points. Prices can be adjusted based on predicted demand.

Price optimization algorithms use machine learning and optimization engines to recommend optimal prices to maximize revenue or other objectives.

A/B testing varying prices provides direct evidence of customer response to different price points.

Analysis of competitor pricing through web scraping and other methods ensures pricing stays aligned with the market.

Visualizations like price waterfalls and price-response curves communicate findings to key executives and stakeholders.

In summary, advanced analytics and data science techniques are powerful tools for better understanding pricing and developing data-driven pricing strategies. However, contextual business knowledge remains critical.