Answer:
The cutoff for a failing score was 40,
Approximately 2.3% of the students failed.
Step-by-step explanation:
Given,
Mean, [tex]\mu=60[/tex]
Standard deviation, [tex]\sigma=10[/tex]
Let x represents the cutoff for a failing score,
Thus, according to the question,
[tex]\frac{x-\mu}{\sigma}=-2[/tex]
[tex]\frac{x-60}{10}=-2[/tex]
[tex]x-60=-20[/tex]
[tex]x=-20+60[/tex]
[tex]x=40[/tex]
Thus, the cutoff for a failing score is 40,
∵ P(<-2) = 0.02275 = 2.275 % ≈ 2.3 %
Hence, Approximately 2.3 % of the students failed.
