

AP Statistics Binomial Practice Test 
1 
) 
Disjointed events are mutually
exclusive. 
2 
) 
If 65% of the voters believe that the president is doing a good job, what is
the probability of selecting a sample of 150 voters in which 55% to 70%
think the president is doing a good job?
binom cdf (150, 0.65, 105) 
binom cdf (150, 0.65, 81) = 91.2% 
3 
) 
Give a distribution, how would you calculate probabilities ?
Find the area under the distribution. 
4 
) 
If there is a 60 % chance that a person will be right, what is the
probability of no more than three being wrong in a 5 person group?
binom cdf (5, 0.4, 3) = 91.3% 
5 
) 
Which of the following are not true about discrete probability
distributions? 


a) Negative probabilities are not possible 


b) The probabilities add up to 1. 


c) The distributions are symmetrical 


d) The standard deviation can have a value that is greater than the mean 


e) All the answers are true. 
6 
) 
Seven people are are seated in a row at the theater. Three have red hair.
How many different ways are there to seat the people with red hair?
nCr = 35 
7 
) 
If 70 % of Americans like country music, what is the probability of having
at least five people in a 20 person group who do not like country music?
p = 1  binomcdf (20, .3, 4) 76.25% 
8 
) 
Albert rolls a single six sided die multiple times. What is the probability
that he gets a six in less than 12 rolls?
geomet cdf (1/6, 11) = 86.54% 
9 
) 
Assume the probability that a golfer will shoot par is 0.3 . What is the
probability that he will shoot par for the 1st time on exactly his 4th hole?
geomet pdf (0.3, 4) = .1029 
10 
) 
Sally and Juan form a golf team. Sally's standard deviation is 4 while
Juan's is 3. What is the standard deviation of their combined scores?
( 4^{2} + 3^{2})^{0.5} = 5,
note that variances can be directly added but not standard deviations. 
11 
) 
Find the mean for a binomial distribution given n = 10, p = 0.8
number = 8 or fraction = 0.8 
12 
) 
Find the standard deviation for a binomial distribution given n = 10, p =
0.8 std dev = 1.265 
13 
) 
Bob's quiz standard deviation is 2 and Martha's is 3. Find the standard
deviation of their combined quiz results. Assume Bob's score is independent
of Martha's. 3.606 
14 
) 
Bob's quiz standard deviation is 2 and Martha's is 3. Find the standard
deviation of the distribution resulting from Bob's quiz score minus Martha's
score on the same quiz. Assume Bob's score is independent of Martha's.
( 2^{2} + 3^{2})^{0.5} = 3.606
, note that even though the 2 scores are subtracted, the variances are
added. 
15 
) 
If 10% of all the apples picked by Martha's are bad. What is the
average number of bad apples that would be found in a barrel of 200 apples?
np = 20 
16 
) 
What is the standard deviation of bad apples in the above problem?
4.243 
17 
) 
What is the probability that there will be no more than 20 bad apples in a
barrel of 200? binom cdf (200, .1, 20) = 55.92% 
18 
) 
What is the probability that Martha will pull out the first bad apple
within the
first three tries (assume replacement)? geomet cdf (.1, 3) = 27.1% 
19 
) 
What is the probability that Martha will pull out the first bad apple on the
second try (assume replacement)? geomet pdf (.1, 2) = 9% 
20 
) 
Describe a geometric distribution?
range is 1 to positive infinity, skewed right, 1 has highest probability 
21 
) 
What is the key difference between a Geometric and binomial distribution? Binomial:
Finds the
probability that k success will occur in n number of
attempts.
 Geometric: Finds the probability
that a success will occur for the first time on the nth try.






