To estimate the mean score of those who took the Medical College Admission Test on your campus, you will obtain the scores of an SRS of students. From published information you know that the scores are approximately Normal with standard deviation about 6.2. You want your sample mean ⎯⎯⎯ to estimate with an error of no more than 1.4 points in either direction.

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What standard deviation must ⎯⎯⎯ have so that 99.7% of all samples give an ⎯⎯⎯ within 1.4 points of ?

Use the 68-95-99.7 rule. Give your answer to four decimal places.