Name: Answers
AP Statistics
Binomial Worksheet #2
1) A manufacturing process produces, on average, 3% defective items. The company ships
12 items in each box and wishes to guarantee no more than one defective item per box.
What is the probability that the box will fail to satisfy the guarantee?
.0487
2) Suppose it is known that 80% of the people exposed to the flu virus will contract the flu. Out of a
family of six exposed to the virus, what is the probability that
a) no one will contract the flu?
.000064
b) all will contract the flu?
.2621
c) at least two will contract the flu?
.9984
3) A pharmaceutical lab claims that a drug it produces causes serious side effects in 20 out of every
1000 people on average. To check this claim, a hospital administers the drug to 15 randomly
selected patients and finds that 3 suffer serious side effects. If the lab’s claims are
correct, what is the probability of the hospital obtaining the results it did?
.0029
4) A manufacturing process produces on average 5 defective items out of 100. To control quality, a
random sample of 60 completed items is selected each day and inspected.
a) Does the inspection constitute a binomial random variable? Explain.
Yes – can be treated as binomial
b) What is the probability that at most two are defected?
.4174
c) How many defective items should the inspector expect to find?
3 items
d) What is the standard deviation of this distribution?
1.69 items
5) A multiple choice test is given with five choices for each of 25 questions. Suppose the test is
answered by guessing.
a) What is the random variable X defined to be?
X is the number of correct guesses
b) What is the probability of getting at least 10 questions correct?
.0173
c) What is the expected number of questions answered correctly by guessing?
5 questions
d) What is the standard deviation of this distribution?
2 questions
e) What is the probability that the number of correctly guessed questions is within one standard
deviation of the mean?
.7927