Excellent Student #1 and 2
Introduction
We picked the topic of California teen laws because we
thought it would be interesting to see how often our
fellow peers break the law. We used calculator
randomization to select the teachers whose classes
we would survey. We surveyed Van Lier’s and Ms.
Sanchez’s classes.
Introduction Continued
Van Lier’s class was given the unbiased survey:
Do you text while driving?
Yes No
Do you stay out past curfew? Yes No
Do you use a Bluetooth while driving? Yes No
If under 18, have you had sexual relations with someone
over 18, or vice versa?
Yes No
Did you drive minors before your year was up? Yes No
Introduction Continued
Ms. Sanchez’s class was given the biased survey:
People who text while driving are 23% more likely to be in a car accident.
Do you text while driving?
Yes
No
Each year, 21% of fatal car crashes involving teenagers between the ages of 16 and 19 were the
result of cell phone usage. This result has been expected to grow as much as 4% every year.
Do you use a Bluetooth while driving? Yes
No
Sixty-three percent of teenage passenger deaths in 2008 occurred in vehicles driven by another
teenager. Among deaths of passengers of all ages, 19 percent occurred when a teenager was
driving.
Did/have you drive/driven minors before your year was up? Yes
No
Sexual relations with a person under the age of consent is in general a criminal offense, with
punishments ranging from community service up to the death penalty.
If under 18, have you had sexual relations with someone over 18, or vice versa? Yes
No
Violators of the curfew law can be fined from $50 to several hundred dollars or charged with a
misdemeanor.
Do you stay out past curfew? Yes
No
Introduction Contd.
Our sample size was big enough because n>30.
Our sample size for both the biased and unbiased
surveys was 34.
Do you text while driving?
YES
NO
UNBIASED .21
.79
BIASED
.91
1
0.9
0.8
0.7
0.6
0.5
0.4
0.3
0.2
0.1
0
.09
Bias: People who text while
driving are 23% more likely to be
in a car accident.
Unbiased
Biased
Yes
No
Do you stay out past curfew?
YES
NO
UNBIASED .71
.29
BIASED
.35
.65
Bias: Violators of the curfew law
can be fined from $50 to several
hundred dollars or charged with a
misdemeanor.
0.8
0.7
0.6
0.5
Unbiased
Biased
0.4
0.3
0.2
0.1
0
Yes
No
Do you use a bluetooth while driving?
YES
NO
UNBIASED
.03
.97
BIASED
.18
.82
Bias: Each year, 21% of fatal
car crashes involving
teenagers between the ages of
16 and 19 were the result of
cell phone usage. This result
has been expected to grow as
much as 4% every year.
1.2
1
0.8
Unbiased
Biased
0.6
0.4
0.2
0
Yes
No
If under 18, have you had sexual relations
with someone over 18, or vice versa?
YES
NO
UNBIASED .21
.79
BIASED
.88
.12
Bias: Sexual relations with a
person under the age of consent
is in general a criminal offense,
with punishments ranging from
community service up to the
death penalty.
1
0.8
0.6
Unbiased
Biased
0.4
0.2
0
Yes
No
Did you drive minors before your year
was up?
YES
NO
UNBIASED
.44
.56
BIASED
.32
.68
0.8
0.7
Bias: Sixty-three percent of
teenage passenger deaths in 2008
occurred in vehicles driven by
another teenager. Among deaths
of passengers of all ages, 19
percent occurred when a teenager
was driving.
0.6
0.5
Unbiased
Biased
0.4
0.3
0.2
0.1
0
Yes
No
Do you text while driving?
2NIP is satisfied because there are two outcomes (yes/no), there is a set number of trials (34),
there are independent variables (survey takers), and a .21 set probability of getting a yes or a
.79 set probability of getting a no.
Problems:
1.Using the binomial formula, find the probability that exactly 4 people will say yes, or P(x=4).
N=34 p=.21 q=.79 x=4.
P(x) = n! / (n – x)!x! • px • qn-x
P(x) = 34! / (34 – 4)!4! • (.21)4 • (.79)34-4
P(x)= .0765567
2.Table: n=15 p=.21 (used .20 on table)
P(x<5)= P(x=1) + P(x=2) + P(x=3)+ P(x=4)
= .132 + .231+ .250+ .188= .801
3. Use your calculator to find P(x>3), or the probability that at least three people will say yes.
- P(x>3)= 1-binomcdf (n,p,x)
- P(x>3)= 1-binomcdf (34, .21, 2) = .9836 or 98.36%.
The probability we get that more than three people will answer yes is .9836, or 98.36%, which
makes sense when looking at our sample size of 34 and the number of people who originally
said yes was 7, or 21%. This is not unusual because 98.36% is greater than 5%.
Identify n, x, p, and q: n=34 x=4 p=.21 q=.79
Mean: n(p)= 34(.21) =7.14
Variance: npq= 34(.21)(.79)= 5.6406
Standard Deviation: Square root of 5.6406 = 2.375
Do you stay out past curfew?
2NIP is satisfied because there are two outcomes (yes/no), there is a set number of trials (34), there are
independent variables (survey takers), and a .71 set probability of getting a yes, and a .29 set probability of
getting a no.
Problems:
1.Using the binomial formula, find the probability that exactly 6 people will say no. n=34 p=.29 x=6
P(x) = n! / (n – x)!x! • px • qn-x
P(x) = 34! / (34-6)!6! • .29x • .7134-4
P (x) = .0547410391
2.Table: n=15 p=.29 (used .30 on table)
P(x<4)= P(x=1) + P(x=2) + P(x=3)
= .031+ .092 + .071= .293
3. Use your calculator to find P(x>6), or the probability that at least six people will say no.
P(x>6)= 1-binomcdf (n,p,x)
P(x>6)= 1-binomcdf (34, .29, 5) = .9564 or 95.64%
The probability we get that more than six people will answer no is .9564, or 95.64%, which makes sense when
looking at our sample size of 34 and the number of people who originally answered no was 10, or 29%. This
is not unusual because 95.64% is greater than 5%.
Identify n, x, p, and q: n=34 x=6 p=.29 q=.71
Mean: n(p)= 34(.29) =9.86
Variance: npq= 34(.29)(.71)= 7.0006
Standard Deviation: Square root of 7.0006 = 2.65
Do you use Bluetooth while driving?
2NIP is satisfied because there are two outcomes (yes/no), there is a set number of trials (34), there
are independent variables (survey takers), and a .03 set probability of getting a yes or .97 set
probability of getting a no.
Problems:
1.Using the binomial formula, find the probability that exactly 21 people will say no. n=34 p=.97 x=21
P(x) = n! / (n – x)!x! • px • qn-x
P(x)=34! / (34-21)!21! • 9721 • .0334-21 .
P(x)=7.80410505E-12
Mean: n(p)= 34(.97) =32.98
Variance: npq= 34(.97)(.03)= .9894
Standard Deviation: Square root of .9894 = .9947
2.Table: n=15 p=.97(used .99 on table)
P(x<6)= P(x=1) + P(x=2)+ P(x=3)+ P(x=4)+ P(x=5)
= 0+0+0+0+0=0
3. Use your calculator to find P(x<2), or the probability that less than two people will say yes.
P(x<2)= binomcdf (n,p,x)
P(x<2)= binomcdf (34, .03, 3) = .9817 or 98.17%
The probability we get that less than two people will answer yes is .9817, or 98.17%, which makes sense
when looking at our sample size of 34 and the percentage of people who originally answered yes
which is 3%. This is not unusual because 98.17% is greater than 5%.
Identify n, x, p, and q: n=34 x=21 p=.03 q=.97
Mean: n(p)= 34(.03) =1.02
Variance: npq= 34(.03)(.97)= .9894
Standard Deviation: Square root of .9894 = .9947
Analysis/Conclusion
 The biased questions did alter the results for all of our questions.
 For texting while driving, 91% said they don’t text for the biased
survey, and 79% said they don’t for the unbiased survey.
 For curfew, more people said they don’t stay out past it when given
the biased survey(35%) compared to the unbiased survey
results(29%).
 More people also said they used bluetooth’s when given the biased
survey(18%). In the unbiased survey, only 3% said they did.
 For the question about having sexual relations with someone over
18, more people said they have not had such relations when given
the biased survey(88%) compared to the 79% for the unbiased.
 And for driving minors before one’s year was up, more people said
no in the biased survey(68%). In the unbiased, 56% said no.
*For this project, we could have distributed more surveys, and we
could have also asked more questions relating to teen laws in our
survey.