Course Content

# Probability Theory Mastering

1. Additional Statements From The Probability Theory

3. Estimation of Population Parameters

4. Testing of Statistical Hypotheses

Probability Theory Mastering

## Challenge: Application of the CLT to Solving Real Problem

*Let's imagine that we need to solve the following problem*:

- Suppose that we come to the shooting range and start shooting, the probability of hitting the target is 0.4, respectively the probability of missing is 0.6.
- We shot 100 times and need to calculate the probability that the hits would be between 50 and 70.

We have a **standard Bernoulli scheme** with two possible outcomes. We can see that solving this problem using the standard Bernoulli scheme will be very problematic since we will have to go through all the possible probabilities in turn, the probability that we hit 50, times hit 51 times, and so on up to 70. That is why we will use the CLT to solve this task.

# Task

In the image above, we showed that the value of interest to us can be approximated using a Gaussian distribution with a mean equal to 40 and a variance equal to 24. Your task is to calculate the required probability: in the first section, we considered that you can use CDF for this. Your task is:

- Import
`norm`

class from`scipy.stats`

module. - Use
`.cdf()`

method of`norm`

class to calculate probability.

Everything was clear?