Answer:
59 to 66
Step-by-step explanation:
Mean test scores = u = 74.2
Standard Deviation = [tex]\sigma[/tex] = 9.6
According to the given data, following is the range of grades:
Grade A: 85% to 100%
Grade B: 55% to 85%
Grade C: 19% to 55%
Grade D: 6% to 19%
Grade F: 0% to 6%
So, the grade D will be given to the students from 6% to 19% scores. We can convert these percentages to numerical limits using the z scores. First we need to to identify the corresponding z scores of these limits.
6% to 19% in decimal form would be 0.06 to 0.19. Corresponding z score for 0.06 is -1.56 and that for 0.19 is -0.88 (From the z table)
The formula for z score is:
[tex]z=\frac{x-u}{\sigma}[/tex]
For z = -1.56, we get:
[tex]-1.56=\frac{x-74.2}{9.6}\\\\ x = 59[/tex]
For z = -0.88, we get:
[tex]-0.88=\frac{x-74.2}{9.6}\\\\ x = 66[/tex]
Therefore, a numerical limits for a D grade would be from 59 to 66 (rounded to nearest whole numbers)
