Explore Westonci.ca, the leading Q&A site where experts provide accurate and helpful answers to all your questions. Discover comprehensive solutions to your questions from a wide network of experts on our user-friendly platform. Join our platform to connect with experts ready to provide precise answers to your questions in different areas.

Let x and s present the sample mean and sample standard deviation, respectively. Is it possible that around 70% of data lie within x-2s and x+2s? (Yes or no)

Sagot :

Using the Chebyshev's Theorem and the Empirical Rule, it is found that it is not possible that around 70% of data lie within x-2s and x+2s.

-------------------------

  • Distributions are classified as symmetric or not symmetric.
  • If the distribution is not symmetric, Chebyshev's Theorem is used, which states that at least 75% of the measures are within 2 standard deviations of the mean.
  • If the distribution is symmetric, the Empirical Rule is used, which states that around 95% of the measures are within 2 standard deviations of the mean.

Thus, from the above bullet points, at least 75% of the measures are within x-2s and x+2s, which means that the percentage of 70% is too small.

A similar problem is given at https://brainly.com/question/23612895