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Over the past 30 years of teaching, a statistics professor found that the distribution of final grades of the students (X) is normal with mean

Over the past 30 years of teaching, a statistics professor found that the distribution of final grades of the students (X) is normal with mean = 70 and standard deviation = 10. Using the books notation, this is written as

X N (70,10). Solve the following problems: (Show all solutions and diagrams, 5 points each).

  1. Find the percentage of students whose scores range from the mean to 85.
  2. Find the percentage of students scoring between 65 and the mean.
  3. Find the percentage of students scoring between 74 and 84.
  4. Find the percentage of students scoring between 62 and 72.
  5. Find the percentage of students who did (a) very well, scoring above 85, and (b) those students who did poorly, scoring below 50.
  6. Find the raw score that bounds the top 10 percent of the distribution.

Show work please.

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