A Business professor decides to give a 10-question true-false quiz to determine who has read an assigned chapter.

A Business professor decides to give a 10-question true-false quiz to determine who has read an assigned chapter. She wants to choose the lowest possible passing grade such that the probability of passing a student who randomly guesses every question is less than 0.2. (A student passes the test if his/her grade is larger than or equal the passing grade.) What score should she set as the lowest passing grade?