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I am a beginner in the field of statistics and data science, so request you to treat me kindly.

Problem statement - Variable X has a mean of 15 and a standard deviation of 2.

What is the minimum percentage of X values that lie between 8 and 17?

I know about 68-95-99.7 empirical rule. From Google I found that percentage of values within 1.5 standard deviations is 86.64%. My code so far:

import scipy.stats
import numpy as np
X=np.random.normal(15,2)

As I understood,

13-17 is within 1 standard deviation having 68% values.

9-21 will be 3 standard deviations having 99.7% values.

7-23 is 4 standard deviations. So 8 is 3.5 standard deviations below the mean.

How to find the percentage of values from 8 to 17?

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    $\begingroup$ if you assume that X is normally distributed, you will get one answer, but since the problem is asking for the minimum, do you think it might mean without assuming that X has a specific distribution such as normal? $\endgroup$
    – John L
    Commented Feb 1, 2021 at 16:58
  • $\begingroup$ Chebyshev's inequality? $\endgroup$
    – BruceET
    Commented Feb 1, 2021 at 18:46

1 Answer 1

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you can use this method for finding your answer:

from scipy.stats import norm


cdf_lower_limit  = norm(15,2).cdf(8)

cdf_upper_limit  = norm(15,2).cdf(17)



probability = cdf_upper_limit - cdf_lower_limit

print(probability)



>> 0.8411121169895074
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