Answer:
The cutoff for a failing score was 40,
Approximately 2.3% of the students failed.
Step-by-step explanation:
Given,
Mean, ![\mu=60](https://tex.z-dn.net/?f=%5Cmu%3D60)
Standard deviation, ![\sigma=10](https://tex.z-dn.net/?f=%5Csigma%3D10)
Let x represents the cutoff for a failing score,
Thus, according to the question,
![\frac{x-\mu}{\sigma}=-2](https://tex.z-dn.net/?f=%5Cfrac%7Bx-%5Cmu%7D%7B%5Csigma%7D%3D-2)
![\frac{x-60}{10}=-2](https://tex.z-dn.net/?f=%5Cfrac%7Bx-60%7D%7B10%7D%3D-2)
![x-60=-20](https://tex.z-dn.net/?f=x-60%3D-20)
![x=-20+60](https://tex.z-dn.net/?f=x%3D-20%2B60)
![x=40](https://tex.z-dn.net/?f=x%3D40)
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.