A study of students taking a20-question exam ranked their progress from one testing period to the next. Students scoring 0 to 5 form group1, those scoring 6 to 10 form group2, those scoring 11 to 15 form group 3 and those scoring 15 to 20 form group 4. The transition matrix to the right shows the result

A) Find thelong-range prediction for the proportion of the students in each group

The proportion of students will be ____% in group1, _____%in group2, ____ %in group 3 , _____in group4

(Type integers or decimals rounded to two decimal places asneeded.)

B) Suppose all students are initially in group 1. When a student reaches group4, the student is said to have mastered the material and is no longertested, so the student stays in that group forever. Find the number of testing periods you would expect for at least70% of the students to have mastered the material.

The number of testing periods is ________

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