We've covered some important distributions thus far: binomial, uniform, poisson, geometric, exponential, and of course, the normal distribution! Now it's time to put those all together and practice selecting the appropriate distribution for various scenarios.

Here's a brief recap:

Binomial Distribution
Given the probability of success (such as flipping a coin; Heads vs Tails) what is the probability of 2 successes on 5 trials?

Uniform Distribution
Everything has equal probability of occuring.

Poisson Distribution
Useful for calculating the probability of a discrete number of events occuring during a given time period. (Generally used when this number is small; as the average grows large the normal distribution becomes a good approximation.)

Geometric Distribution
Related the binomial distribution and bernoulli trials. Rather then asking the probability of X success in Y trials, asks for the probability that the first success is on the nth trial.

Exponential Distribution
Has a memoryless property where the probability of success in the next block of time is the same whether or not another success just happened, or a substantial period of time has already passed. If the total expected number of events is poisson distributed, the time between events is exponentially distributed.

Normal Distribution
The classic [symmetrical] bell shaped curve. Also known as the Gaussian distribution. Often the assumed distribution for unknown variables (including error).

A car sales person sells an average of 2 cars per week. What's the probability that he/she sells 4 in a given week?

#Your code here

What's the probability that the car salesperson sells 0 cars in a given week?

#Your code here

Whats' the probability that the car salesperson sells 0 cars in 2 consecutive weeks?

#Your code here

The sales associate is worried about not getting paid for a period of time. What's the probability that 2 weeks (or more) pass between selling one car and the next?

#Your code here

Below is a sample of SAT scores (yes SAT scores are now out of 2400 not 1600): Assuming the sample is representative, what would be the estimated percentile rank be of someone who scored a 2000?

import numpy as np

 scores = [1710, 1460,2060,1010,1690,1080,1940,1050,1020,1280,
 1240,1570,1690,910,1570,1440,1530,1700,1750,1320,
 2050,1430,1340,960,1480,890,1620,1280,1750, 1490]

#Your code here

Assuming that you're using a fair coin, what's the probability of flipping 8 heads on 10 flips?

#Your code here

What's the probability that you have to flip a coin 5 times in order to get the first head?

#Your code here

Assuming the train system is on a perfect schedule where trains show up exactly every 10 minutes (ignoring reality). What is the probability that a rider who randomly shows up has to wait at least 3 minutes for a train?

#Your code here