Quiz Bowl Formatted Questions On Binomial And Geometric Distributions ANSWERS
1. Setup: McDonald’s Happy Meals come with a Teenage Mutant Ninja Turtle in each meal.
Emma has collected seven of the eight different toys and begs for her mother to buy more happy
meals so that she can get Raphael, the only Ninja not in her collection. If every meal has a toy,
and the toys are distributed randomly among the meals:
Q: How many meals do you expect her mother will have to buy in order to get the missing toy?
8
Q: Find the probability that she will get Raphael before the sixth meal is bought. 0.4870
Q: Find the probability that she will not get Raphael until after she has already bought 5 meals.
0.5129
Q: Find the probability that she will get Raphael in her first Happy Meal. 0.125
2. Setup: A distribution is binomial with n = 16 and p = .1 .
Q: Describe the distribution.
skewed right with a mean of 1.6 and a standard deviation of 1.2.
The distribution is
Q. Would a normal distribution be a good model for this? No, the strong skew makes this very
different from a normal distribution.
3. Setup: A distribution is binomial with
n = 4 and p = .8 .
Q: Describe the distribution. The
distribution is skewed left with a mean of 3.2
and a standard deviation of 0.8.
Q. Would a normal distribution be a good
model for this? No, again, the skew prevents
this from being approximately normal.
4. Setup: A distribution is binomial with n = 25 and p = .3.
Q: Describe the distribution. The distribution is very symmetrical (but with a slight right skew)
with a mean of 7.5 and a standard deviation of 2.2912.
Q. Would a normal distribution be a good model for this? It looks somewhat close to normal, so
an approximation would not be so bad, but fails the Rules of Thumb, because np < 10 .
5. Setup: A distribution is binomial with n = 30 and p = .6 ,
Q: Describe the distribution.
The distribution is very
symmetrical (with a slight left
skew) with a mean of 18 and
a standard deviation of
2.6832.
Q. Would a normal
distribution be a good model
for this? Yes, this looks
approximately normal and
passes the Rule of Thumb, as np > 10 and n(1- p) > 10 .
6. Setup: According to Martha White in Time magazine,
http://business.time.com/2012/04/12/college-students-are-credit-card-dunces/ 70% of undergraduate
students have credit cards, and of those, only 10% pay their balances in full each month, thereby
avoiding paying interest and fees. A random sample of 500 cardholders is selected. Of interest is the
variable X, which is the number of students in the sample who pay in full each month.
Q: What is the mean of X? 50
Q: What is the standard deviation of X? 6.7082
Q. What is the probability that fewer than 50 students pay in full each month? 0.4781
Q. What is the probability that more than 50 students pay in full each month? 0.4624
7. Setup: Jack is trying to get help with an AP chemistry question as he sits with a group of AP
math student friends. He randomly asks students if they have taken AP chemistry and 60% of
this student population have. He will stop asking when he finds a student who has taken AP
chem.
Q: What is the probability that the first student who has taken AP chem is the 2nd student he
asks? 0.24
Q: How likely is it that will ask 4 or fewer students until he finds one who has taken AP chem?
0.9744
Q: What is the probability that he will have to ask more than 3 students to find one who has
taken AP chem? 0.064
8. Setup: An experiment was conducted to investigate whether a handwriting analyst could
distinguish a normal person’s handwriting from that of a serial killer. A well-known expert was
given 10 files, each containing handwriting samples from a normal person and a known serial
killer. The analyst was asked to identify the serial killer’s handwriting.
The analyst was right 6 out of 10 trials. We would like to know whether the analyst has the
ability to distinguish the handwriting of serial killers and normal persons.
Q: What is the probability of guessing correctly 6 out of 10 times if the probability of a correct
guess is .5? 0.2050
Q: What is the probability of guessing correctly 6 or more out of 10 times if the probability of a
correct guess is .5? 0.3769
Q: What is the probability of guessing correctly 6 or more out of 10 times if the probability is .8?
0.9672