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 is0.6; - We shot 100 times and needed to calculate the probability that the hits would be between
50and70.
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.
Swipe to start coding
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
normclass fromscipy.statsmodule. - Use
.cdf()method ofnormclass to calculate probability.
Рішення
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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 is0.6; - We shot 100 times and needed to calculate the probability that the hits would be between
50and70.
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.
Swipe to start coding
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
normclass fromscipy.statsmodule. - Use
.cdf()method ofnormclass to calculate probability.
Рішення
Перейдіть на комп'ютер для реальної практикиПродовжуйте з того місця, де ви зупинились, використовуючи один з наведених нижче варіантівДякуємо за ваш відгук!
single
