The central limit theorem implies which of the following:   a. The averages of many random samples (of a given sample size n) from the same population are approximately normally distributed, but only if the population is normally distributed.     b. The averages of many random samples (of a given sample size n) from the same population are approximately normally distributed with mean μ and standard deviation σ / √n , but only if the population is normally distributed.     c. The averages of many random samples (of a given sample size n) from the same population are approximately normally distributed, regardless of the shape of the population distribution, provided that n is sufficiently large.     d. None of these choices are true.

Practical Management Science
6th Edition
ISBN:9781337406659
Author:WINSTON, Wayne L.
Publisher:WINSTON, Wayne L.
Chapter10: Introduction To Simulation Modeling
Section10.2: Probability Distributions For Input Variables
Problem 2P: Use Excels functions (not @RISK) to generate 1000 random numbers from a normal distribution with...
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The central limit theorem implies which of the following:

  a. The averages of many random samples (of a given sample size n) from the same population are approximately normally distributed, but only if the population is normally distributed.  
  b. The averages of many random samples (of a given sample size n) from the same population are approximately normally distributed with mean μ and standard deviation σ / √n , but only if the population is normally distributed.  
  c. The averages of many random samples (of a given sample size n) from the same population are approximately normally distributed, regardless of the shape of the population distribution, provided that n is sufficiently large.  
  d. None of these choices are true.
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