A set of final examination grades in an introductory statistics cours is normally distributed, with a mean of 73 and a standard deviation 8 . (a) What is the probability that a student scored below 91 on this exam (b) What is the probability that a student scored between 65 and 89 ? (c) The probability is \( 5 \% \) that a student taking the test scores higher th what grade? (d) If the professor grades on a curve (i.e., gives A's to the top \( 10 \% \) of class, regardless of the score), are you better off with a grade of 81 this exam or a grade of 68 on a different exam, where the mean is 6 and the standard deviation is 3? Show your answer statistically and explain.
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