Math Solutions

[Steps Shown] ACT scores of high school seniors. The scores of high school seniors on the ACT college entrance examination in 2003 had mean μ=20.8 and standard

Question: ACT scores of high school seniors. The scores of high school seniors on the ACT college entrance examination in 2003 had mean \(\mu=20.8\) and standard deviation \(\sigma=4.8 .\) The distribution of scores is only roughly Normal.

  1. What is the approximate probability that a single student randomly chosen from all those taking the test scores 23 or higher?
  2. Now take an SRS of 25 students who took the test. What are the mean and standard deviation of the sample mean score \(\bar{x}\) of these 25 students?
  3. What is the approximate probability that the mean score \(\bar{x}\) of these students is 23 or higher?
  4. Which of your two Normal probability calculations in (a) and (c) is more accurate? Why?

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