How to find the probability for Normal distribution.
ACT scores of high school seniors and the scores of high school seniors on the ACT college entrance examination in 2003 had mean JL = 20.8 as well as standard deviation (J = 4.8. The spreading of scores is only roughly Normal.
(a) Explain what is the approximate probability that a single student randomly chosen from all those taking the test scores 23 or higher?
(b) Currently take an SRS of 25 students who took the test. Explain what are the mean and standard deviation of the sample mean score x of these 25 students?
(c) Explain what is the approximate probability that the mean score x of these students is 23 or higher?
(d) Explain which of your two Normal probability calculations in (a) and (c) is more accurate and Why?