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Hey I have attached my questions and the answer sheet. Please let me know if you can help

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 1. A school administrator wonders if students whose first language is not English score differently on the math portion of the sat exam than students whose first language is English. The mean SAT math score of students whose first language is english is 516 on the basis of data obtained from the college board. A simple random sample of 20 students whose first language is not English result in a sample mean SAT math score of 522. SAT math score are normally distributed with a population standard deviation of 114. Why is it necessary for SAT math scores to be normally distributed to test the hypothesis?
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