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.

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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.
Transcribed Image Text: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.
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