The State University of Columbia just announced the average ACT scores of its enteringfreshman class of 12,000 students is 27. Assume a standard deviation of 3.8. We aresuspicious of this claim, so we take a random sample of 50 of its freshmen and calculatethe sample average ACT score, , to be 24.9. Using the Central Limit Theorem and ourprobability calculations, show an analysis of the data. How believable is the claim ofState University?(Hint: use the claim of ì=27 and ó=3.8 as the population parameters.)

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