Normal distribution and standard deviation

A professor would like to use the normal distribution to assign grades such that 5% of students receive A's.  If the exam average is 62 with a standard deviation of 13, what grade should be the cutoff for an A? 

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95% will be 1.645 standard deviations above the mean = 62 + 1.645 x 1.3 = 83.3 so a grade of 84 or higher should get an A.

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