Question 7

7. One semester I gave a 20-question test for psychic powers to a class of 80 students. Each student (independently) guessed "left" or "right," then (using the random number generator in R) a star appeared on either the left or the right side on the screen. This process was repeated 20 times. At the end, each student counted up the number of times they correctly guessed the side of the screen the star would appear on. The highest score was 15. a) (4 points.) Suppose this test is taken by a student who does not have psychic powers. What is the probability she gets 15 or more correct? b) (4 points.) Suppose this test is taken by eighty students who do NOT have psychic powers. What is the probability at least one student gets 15 or more correct