Question: New bow, again. The archer in Exercise I continues shooting arrows, ending up with 45 bull s-eyes in 50 shots. Now are you convinced that the new bow is better? Explain.
Exercise I: New bow. Our archer in Exercise II purchases a new bow, hoping that it will improve her success rate to more than 80% bull s-eyes. She is delighted when she first tests her new bow and hits 6 consecutive bull s-eyes. Do you think this is compelling evidence that the new bow is better? In other words, is a streak like this unusual for her? Explain.
Exercise II: Arrows. An Olympic archer is able to hit the bull s-eye 80% of the time. Assume each shot is independent of the others. If she shoots 6 arrows, what's the probability of each of the following results?
a) Her first bull s-eye comes on the third arrow.
b) She misses the bull s-eye at least once.
c) Her first bull s-eye comes on the fourth or fifth arrow.
d) She gets exactly 4 bull s-eyes.
e) She gets at least 4 bull s-eyes.
f) She gets at most 4 bull s-eyes.