Name: Answers
AP Statistics
Binomial Worksheet #1
1) An Olympic archer is able to hit the bull’s-eye 80% of the time. Assume that each shot is
independent of the others. If she shoots 6 arrows, what is the probability of each result below?
a) She gets exactly 4 bull’s-eyes.
.2458
b) She gets at most 4 bull’s-eyes.
.3446
c) She gets at least 4 bull’s-eyes.
.9011
d) She misses the bull’s-eye at least once.
.7379
2) Assume that 13% of people are left-handed. If we randomly select 12 people from this population,
a) what is the probability that they are not all right-handed?
.8120
b) what is the probability that there are no more than 10 righties?
.4748
c) what is the probability that there are exactly 6 of each?
.0019
d) what is the probability that the majority is right-handed?
.9978
3) A wildlife biologist examines ducks for a genetic trait he suspects may be linked to sensitivity to
industrial toxins in the environment. Previous research had established that this trait is found in
one of every 8 ducks. He collects and examines a dozen ducks. If the frequency of the trait
has not changed, what is the probability he finds the trait in
a) none of the ducks?
.2014
b) at least 2 ducks?
.4533
c) 3 or 4 ducks
.1707
d) no more than 4 ducks
.9887
4) A newly hired telemarketer is told he will probably make a sale on about 12% of his phone
calls. The first week he called 200 people, but only made 10 sales. Should he suspect he
was misled about the true success rate? Explain.
P(X=10) = .00039
Yes, he should suspect he was misled since the probability is so low.
5) An airline, believing that 5% of passengers fail to show up for flights, overbooks (sell more tickets
than there are seats). Suppose a plane will hold 265 passengers, and the airline sells 275 seats.
What’s the probability that the airline will not have enough seats so someone gets bumped?
P(X>265) = .1155