Challenge: Application of the CLT to Solving Real Problem | The Limit Theorems of Probability Theory
Probability Theory Mastering

Course Content

Probability Theory Mastering

Challenge: Application of the CLT to Solving Real Problem

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

1. 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`;
2. We shot 100 times and needed 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.

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:

1. Import `norm` class from `scipy.stats` module.
2. Use `.cdf()` method of `norm` class to calculate probability.

Everything was clear?

Section 2. Chapter 5

Challenge: Application of the CLT to Solving Real Problem

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

1. 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`;
2. We shot 100 times and needed 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.

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`.
1. Import `norm` class from `scipy.stats` module.
2. Use `.cdf()` method of `norm` class to calculate probability.