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<em>Answer:</em>
<em>For grade A ,a student needs Z score of 2 or above, the required score is</em>
<em> X = 68 + 12Z =92, For grade B, a student needs Z score between 1 and 2 . </em>
<em> The required score is = 68 + (12 * 1) < X = 68 + ( 12 * 2) = 80 < X < 92, For grade C ,a student needs Z score between -1 and 1 . The required score is = 68 + ( 12 * x - 1) < X = 68 + (12 * x 1) = 56 <X<80. For the grade D, a student needs Z score between -2 and -1 . </em>
<em> The required score is = 68 + (12 * x -2) < X = 68 + (12 * x -1) = 44< X< 56</em>
Step-by-step explanation:
<em>From the given question, </em>
<em>let the rv X represent student's score.</em>
<em>Z = x - 68/12 ~ N (0,1 )</em>
<em>Now, we know for a standard normal distribution</em>
<em>Thus,</em>
<em>For grade A ,a student needs Z score of 2 or above, the required score is</em>
<em> X = 68 + 12Z =92</em>
<em>For grade B, a student needs Z score between 1 and 2 . </em>
<em> The required score is = 68 + (12 * 1) < X = 68 + ( 12 * 2) = 80 < X < 92</em>
<em>For grade C ,a student needs Z score between -1 and 1 . </em>
<em> The required score is = 68 + ( 12 * x - 1) < X = 68 + (12 * x 1) = 56 <X<80</em>
<em>For the grade D, a student needs Z score between -2 and -1 . </em>
<em> The required score is = 68 + (12 * x -2) < X = 68 + (12 * x -1) = 44< X< 56</em>
<em>For student with score less 44 gets an F.</em>
<em>Note: find an attached image for the graphic sketch of the normal distribution.</em>
