You may have taken classes where the exam grades are scaled. One way to scale grades is to use a normal distribution. Suppose an instructor found the mean exam score of 64 and a standard deviation of 14.2 points and the distribution of the exam scores appeared to be normally distributed. Using this information, answer each of the following:

a. If a student scores at least 1.5 standard deviations above the mean, they will receive the grade of \(\mathrm{A}\). What percentage of students will receive the grade of \(\mathrm{A}\) ?

b. If a student scores from 0.5 to 1.5 standard deviations above the mean, they will receive the grade of \(\mathrm{B}\). What percentage of students will receive the grade of \(\mathrm{B}\) ?

c. If a student scores from 0.5 standard deviations below the mean to 0.5 standard deviations above the mean, they will receive the grade of \(C\). What percentage of students will receive the grade of \(C\) ?

d. If a student scores more than 1.5 standard deviations below the mean, they will receive the grade of F. What percentage of students will receive the grade of F?