Math 107 Final Exam and Solutions May 10, 2001 ProfessorSpruckb. (15 pts) EvaluateR∞31x2-x-2dxAx-2+Bx+1to findA=1c.(15 pts) Assume that a random variable X has a normal distribu-tion with mean 12 and standard deviation 4.Find the probability that5.6< X <19.2 using the Z-table at the end of your exam paper.1
2. (20 pts) Lety0(t) = 10-y(t), y(0) = 0. Findy(t) and show thatits asymptotic limit is 10 ast→ ∞. How long does it take for y(t) to reach87.5% of its asymptotic limit? Justify your answer.