To compensate for disorientation in zero gravity, astronauts rely heavily on visual information to establish a top-down orientation. The potential of using color brightness as a body orientation clue was studied in Human Factors (Dec. 1988). Ninety college students, reclining on their backs in the dark, were disoriented when positioned on a rotating platform under a slowly rotating disk that blocked their field of vision. The subjects were asked to say “stop” when they felt as if they were right-side up. The position of the brightness pattern on the disk in relation to each student’s body orientation was then recorded. Subjects selected only three disk brightness patterns as subjective vertical clues: (1) brighter side up, (2) darker side up, and (3) brighter and darker side aligned on either side of the subjects’ heads. Based on the study results, the probabilities of subjects selecting the three disk orientations are .65, .15, and .20, respectively. Suppose n =8 subjects perform a similar experiment.
a. What is the probability that all eight subjects select the brighter-side-up disk orientation?
b. What is the probability that four subjects select
the brighter-side-up orientation, three select the darker side up orientation, and one selects the aligned orientation?
c. On average, how many of the eight subjects will select the brighter-side-up orientation?