AP STATISTICS
Quiz-CH 6 REVIEW
Last 4 of Student ID____________
Period______
1. One treatment has a 60% success rate in helping people stop smoking.
a) Find the probability of successfully treating 3 smokers in a group of 8 smokers.
P(X=3) binompdf(8,.6,3)=0.1239
b) In a group of 25 smokers what is the probability that no more than 6 will be unable to stop smoking?
P(X≤6) binomcdf(25,.4,6)=0.0736
2. In a certain college, 64% of the entering freshmen graduate.
a) Find the probability that of 10 randomly selected entering students, exactly 7 will graduate.
P(X=7) binompdf(10,.64,7)=0.2462
b) Find the probability that at least 8 will graduate.
P(X≥8) 1 – binomcdf(10,.64,7)=0.2405
c) What is the expected number who will not graduate?
µX=np=10(.36)=3.6
3. A study of college enrollments shows that 40% of all full-time undergraduates are under 20 years of age.
a) If 20 full-time undergraduates are randomly selected, what is the probability that at least half are
under 20?
P(X≥10) 1 – binomcdf(20,.4,9)=0.2447
b) In a sample of 20, what is the mean number of undergraduates under 20?
µX=np=20(.4)=8
c) What is the standard deviation for a sample of 20?
𝝈X=√𝒏𝒑(𝟏 − 𝒑) = √𝟐𝟎(. 𝟒)(. 𝟔)=2.1909
4. Sparkle Farkle is taking her written test to get her license. There is an 85% probability of passing the
test.
a) What is the probability that she will pass on her first try?
P(X=1) geometpdf(.85,1)=0.85
b) What is the probability that it will take her no more than 2 tries?
P(X≤2) geometcdf(.85,2)=0.9775
5. Fred Berful is a recent law school graduate who intends to take the state bar exam. According to the
National Conference on Bar Examiners, about 57% of all people who take the state bar exam pass. (The
Books of Odds, Signet 1993).
a) What is the probability that Fred first passes the bar exam on the second try?
P(X=2) geometpdf(.57,2)=0.2451
b) What is the probability that Fred needs more than three attempts to pass?
P(X>3) 1 – geometcdf(.57,3)=0.0795
6. A probability distribution is given at the right
x
5
10
20
p(x) .6
?
.1
a) Find the missing probability.
1-(0.6+0.1)=0.3
b) Find the expected value of the random variable.
E(X)=8 (same as mean, 𝐱̅)
c) What is the standard deviation?
SD(X)=4.58 (same as standard deviation, 𝝈𝒙)
d) If a new random variable is defined as Y = 56 + 7X, calculate E(Y), VAR(Y) and SD(Y).
E(Y)=112 (same as mean, 𝐱̅)
SD(Y)=32.078 (same as standard deviation, 𝝈𝒙)
VAR(Y)=1028.998 (same as (𝝈𝒙)𝟐)
7. Anthropological studies at Casa del Rito Pueblo indicate that approximately 5% of all pot shards at the
excavation site are from the traditional type of pottery know as Socorro black on white ( Bandelier
Archaeological Excavation, Summer 1990, Washington State University). What is the probability that
a) the fifth shard examined is the first one that is Socorro black on white?
P(X=5) geometpdf(.05,5)=0.0407
b) the first Socorro shard is found on the tenth trial?
P(X=10) geometpdf(.05,10)=0.0315
c) more than three pot shards have to be examined before finding the first Socorro black on white?
P(X>3) 1 – geometcdf(.05,3)=0.8574
8. Police find that one patrol unit gets a 2% arrest record when it sets up a checkpoint for drunk drivers.
a) What is the probability that of 20 drivers, there will be exactly one arrest?
P(X=1) binompdf(20,.02,1)=0.2725
b) If 250 drivers pass through the checkpoint, what is the expected number of arrests?
µX=np=250(.02)=5
c) What is the standard deviation of the situation in part b)?
𝝈X=√𝒏𝒑(𝟏 − 𝒑) = √𝟐𝟓𝟎(. 𝟎𝟐)(. 𝟗𝟖)=2.2136
d) What is the probability that the third driver through the checkpoint is the first one arrested?
P(X=3) geometpdf(.02,3)=0.0192
e) What is the probability that the police need to check no more than 10 drivers before making an arrest?
P(X≤10) geometcdf(.02,10)=0.1829
9. The weight of a “16 oz” bag of chocolate chip cookies can be viewed as a random variable with an
approximate normal distribution with actual mean of 16.1 ounces and a standard deviation of 0.1 ounce.
a) What is the probability that a randomly selected bag will be underweight (less than 16.0 ounces)?
P(X<16) normalcdf(0,16,16.1,0.1)=0.1587
b) What is the probability that a randomly selected bag will be over 16.2 ounces?
P(X>16.2) normalcdf(16.2,100,16.1,0.1)=0.1587