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  1. Prepare
  2. Artificial Intelligence
  3. Probability & Statistics - Foundations
  4. The Central Limit Theorem #3
  5. Discussions

The Central Limit Theorem #3

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  • petitmath
     + 0 comments

    python3 solution with scipy.stats yields 0.7887, deemed incorrect by the checker.

  • madhusudanxtreme
     + 0 comments

    n = 100 s = 80 u = 500 sample_s = 80/10 = 8 e are given µ = 500, σ = 80, n = 100. a. P(490 < x <¯ 510) = P((490−500)/(√80/100)< z < (490−500)/(√80/100)) = P(−1.25 < z < 1.25) = 0.8944 − (1 − 0.8944) = 0.7888.

  • vikashvermacom92
     + 0 comments
    • n = 100
    • s = 80
    • u = 500
    • sample_s = 80/10 = 8
    • p(490
    • p(x<510) = (510-500)/8 = 10/8 = 1.25
    • p(-1.25

  • deankiss
     + 0 comments
    import math

def cdf(x, mu, sigma):
    return 0.5 + math.erf((x-mu)/(sigma*2**0.5))*0.5

n_samples=100
lower_bound = 490
upper_bound  =510
population_mu = 500
population_sigma = 80

sample_mean_mu=population_mu
sample_mean_sigma=population_sigma/n_samples**0.5

Prob_l = cdf(lower_bound, sample_mean_mu, sample_mean_sigma)
Prob_u = cdf(upper_bound, sample_mean_mu, sample_mean_sigma)

print('{:0.4f}'.format(Prob_u-Prob_l))

  • pWiszniewski
     + 0 comments

    According to CTG, if you have X1...Xn independent variables with same distribution (here it's N(500,80)), their mean X has a normal distribution N( µ; σ/sqrt(n)) (sorry, can't write proper math symbols in browser) So in this case we have µ = 500, σ = 80, sqrt(n) = 10. So mean of X has the distribution of N(500;8)

    Now once you have a distribution, you need to calculate P(490 < mean X < 510) Once you normalize, it's P (-1.25 < Z < 1.25). That should be easy to calculate