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- Prepare
- Artificial Intelligence
- Probability & Statistics - Foundations
- Day 4: The Central Limit Theorem #1
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# Day 4: The Central Limit Theorem #1

# Day 4: The Central Limit Theorem #1

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The checker accepts an incorrect answer, although 0.0098 should be the correct answer.

import scipy.stats as st import math

pop_mean = 205 pop_sd = 15 sample_size = 49 x = 9800/49

sample_sd = pop_sd/math.sqrt(sample_size)

z_score = (x-pop_mean)/sample_sd

prob = st.norm.cdf(z_score)

print( '{:0.4f}'.format(prob))

The central limit theorem states that for a large number of independent random variables, the mean of their sum will approach the mean of the sum of the individual random variables as the number of random variables increases.

p(xmean<=200)=P(Z<=(200-205)/(15/7))=P(Z<=-7/3) and find the corresponding probability in R

`pnorm(-7/3`

) is 0.0098