Assignment 6 - MATH 203 - Fall 2020-2021 Deadline: 10.01.2021, 23:00 1) A manufacturer will purchase a battery from one of two suppliers. This manufacturer will get the battery from supplier 1 with probability 0.6 and from supplier 2 with probability 0.4. A battery obtained from supplier 1 has a lifetime, which is exponentially distributed with a mean of 6 months. On the other hand, the lifetime of a battery from supplier 2 is again exponentially distributed with a mean of 5 months. What is the probability that the purchased battery (from supplier 1 or 2 with aforementioned probabilities) will last more than 5 months? 2) In a course, there are 2 midterm exams and 1 final exam. Grades obtained from these exams are indepen- dent and normally distributed with following means and standard deviations: Midterm 1: Mean and standard deviation are 65 and 20, respectively. Midterm 2: Mean and standard deviation are 60 and 25, respectively. Final: Mean and standard deviation are 40 and 15, respectively. In the calculation of overall grades, we take % 30 of grades of each midterm and % 40 of the grade of the final exam. If the passing grade is 40 (i.e., overall grade should be at least 40 to pass from this course), find the proportion of students who will fail from the course.