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Exam 1---Math 2210---Fall 2013
Directions: Follow all directions. Show all work where necessary (excluding computations done
exclusively on the calculator) neatly in detail to ensure proper credit. Problems with no work where
work is indicated may receive no credit.
1. The College of Science and Mathematics at GRU is home to the departments of Mathematics,
Chemistry/Physics, Biology, and Psychology. Now that all new students are getting advised through
the Advising Center, the administration at GRU wants to see if each student makes at least one
appointment with an academic advisor this semester, and the administration believes that 85% of the
students will meet with an advisor at least once. A sample of 15 Mathematics students, 20
Chemistry/Physics students, 50 Biology students, and 35 Psychology students is taken (to take into
account the different size of each of the programs). Of these 120 students, 82 of them (about 68%)
end up scheduling at least one advising appointment.
a. The variable under consideration is (underline one):
The number of advising appointments made by each student.
The number of students who made an advising appointment.
Whether or not each individual student made at least one advising appointment.
b. The type of sampling that was used was (underline your answer):
Systematic
Stratified
Cluster
c. The “68%” figure is a
Parameter
Statistic
d. The “85%” figure is a
Parameter
Statistic
2. The data below tells you the number of regular season points scored by the New England Patriots
during each of the 13 years Bill Belichick (a.k.a. the Evil One) has been their head coach.
557 379 513 437 518 348 427 381 410 371 589 276 385 Find the mean, median, the third quartile and the sample standard deviation of this data set. Be sure
to clearly label what is what.
3. Scores on the SAT exam (Math+Writing+Critical Reading) have mean 1518 and standard
deviation 325. Scores on the ACT exam have mean 21.1 with standard deviation 4.8.
a. Find the z-score associated with an SAT score of 1840.
b. Find the z-score associated with an ACT score of 26.0.
c. Relatively speaking, which is the better score-the 1840 on the SAT or the 26 on the ACT? Explain
briefly (one concise, properly written sentence should suffice).
d. Use Chebyshev’s Theorem to find an interval where at least 75% of the ACT scores must fall.
4. A Chemistry student for their own inscrutable reasons wants to see how much tar is contained in
unfiltered cigarettes. The sample 25 cigarettes and measure how much tar is in each of them. The
data is below.
Midpoint of this class
Amount of tar present (mg)
10-13
14-17
18-21
22-25
26-29
Frequency
1
0
15
7
2
a. Using the midpoint of each class of data, estimate the mean and sample standard deviation of this
sample data. Humor me and include units on the answers.
b. The term that best describes the distribution of the data is (underline one):
BIMODAL
UNIFORM
SYMMETRIC
SLIGHTLY SKEWED
5. On the TV show Hell’s Kitchen, a group of chefs (split into two teams-the Red team and the Blue
team) attempt to complete a dinner service to 200 diners under the profanity-laced supervision of
chef Gordon Ramsay. One evening, Ramsay hands out comment cards to the diners to see their
opinion of the food.
Team
Red Team (R)
Blue Team (B)
Food
Excellent (E)
60
30
Rating
Fair (F)
35
30
Dog’s Dinner (D)
5
40
If you pick a diner at random from this population, find…
a. P(E) , the probability they found the food excellent.
b. P(E|B), the probability the food was excellent, given that it was prepared by the blue team.
c. P(B|E)
d. Are B and E independent events?
6. On the Big Bang Theory, the characters sometimes play a variation of the game rock-paperscissors called “rock-paper-scissors-lizard-Spock”. Two players each select one of the 5 choices, and
assume it is equally likely that either player will make any of the 5 available choices. If the two
players make the same choice, the game is a tie.
The sample space and rules for the game is below.
1-Player 1 wins
Player 2
2-Player 2 wins
Rock
Scissors
Paper
Lizard
Spock
Rock
T
1
2
1
2
Find the probability that…
a. A given play of the game is a tie.
b. Player 1 wins any given game.
c. Both players select “lizard”.
d. Neither player selects “rock”.
T-game is a tie
Scissors
2
T
1
1
2
Player 1
Paper
1
2
T
2
1
Lizard
2
2
1
T
1
Spock
1
1
2
2
T
7. Answer each question by underlining your response.
a. In the game of Texas Hold Em, each player is dealt two cards from a 52-card deck. Since there
are 1326 equally likely two-card hands, and exactly 78 of them are ‘pocket pairs’ (two cards of the
same rank), the probability of being dealt a pocket pair on any given hand is 78/1326 5.9%.
The interpretation of probability used here is the:
Classical Interpretation
Relative Frequency Interpretation
Subjective Interpretation
b. You sit down to take an exam. Going into the test, you believe there is an 80% probability you
will earn an A on the test. However, you find yourself unable to answer the very first question.
Thus, you conclude that your probability of getting an A on the test is now considerably lower than
80%.
The interpretation of probability used here is the:
Classical Interpretation
Relative Frequency Interpretation
Subjective Interpretation
c. Dr. Smith is recapping the result of this exam, and he notes that 40% of the students scored
higher than 90, and 40% of the students scored between 60 and 70.
The distribution of the exam scores is:
Uniform
Symmetric
Skewed
Bimodal
d. There was a feature on the local news the other day about GRU’s child care center. Apparently it
got a high rating from some state agency. An employee of the child care center pointed out that
children who enroll in such highly-rated centers tend to graduate college at a higher rate than
children who do not.
Obviously, making sure one’s children are adequately supervised probably carries some benefit (or
says something positive about the way they’re being raised!), but making sure a 3 year old is babysat
properly does not ensure the child will graduate from college 18 years in the future, as a thousand
other contributing factors are certainly in play.
What form of bias is illustrated here?
Confounding
Sampling error
Self-selection