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Exam scores are a key measure for evaluating student performance. A national education board assesses student achievement by analyzing scores from a standardized test. In 2023, the scores of all students in a particular grade were normally distributed with a mean of 75 points and a standard deviation of 5 points.
Using this information, calculate the following probabilities or values for the students' scores:
  1. The percentage of students with scores between 70 and 75 points.
    \(\pourcent\)
  2. The percentage of students with scores between 65 and 75 points.
    \(\pourcent\)
  3. The percentage of students with scores less than 80 points.
    \(\pourcent\)
  4. In 2024, if there were 600 students in this grade, estimate the number of students with scores between 70 and 85 points. (
    ! e \(\pi\) ( ) % AC sin cos tan 7 8 9 / \(\sin^{-1}\) \(\cos^{-1}\) \(\tan^{-1}\) 4 5 6 * \(x^2\) \(\sqrt{\phantom{2}}\) xy 1 2 3 - ln exp log 0 . = +
    and round to the nearest integer.)
    students
For a normal distribution, the coverage probabilities are illustrated below: