Question: A college admissions officer wanted to know the average Scholastic Aptitude Test (SAT) score of this year’s class of entering students. Rather than checking all student folders, she decided to use a randomly chosen sample. If it is known that student scores are normally distributed with a standard deviation of 70, how large a random sample is needed if the admissions officer wants to obtain a 95 percent confidence interval estimate that is of length 4 or less?

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