THE FIRST EXAM
MATH 311, SPRING 2005
APRIL 19, 2005
NAME: ________________________________
_____________________________________________________________________________________________________________
 ALL PERTINENT WORK MUST BE SHOWN NEATLY AND CORRECTLY. POINTS WILL BE DEDUCTED FOR INCORRECT, MISSING, OR
UNCLEAR WORK REGARDLESS OF THE FINAL ANSWER.
 COMPLETE ENGLISH SENTENCES MUST BE GIVEN FOR ALL “SHORT ANSWER” TYPE QUESTIONS.
 DRAW A CIRCLE OR A BOX AROUND YOUR ANSWER.
1. The U.S. Army reports that the distribution of head circumference among male soldiers is approximately
normal with mean 22.8 inches and standard deviation 1.1 inches.
a. (6 points) What percentage of male soldiers has a head circumference greater than 22 inches?
Answer: _____________________________________
2. (4 points) Which of the following is likely to have a mean that is smaller than the median?
a. The salaries of all National Football League players.
b. The scores of students (out of 100 points) on a very easy exam on which most score perfectly, but a
few do very poorly.
c. The prices of homes in a large city.
d. The scores of students (out of 100 points) on a very difficult exam on which most score poorly, but a
few do very well.
e. none of the above
3. (6 points) A fair coin (one for which both the probability of heads and the probability of tails are 0.5)
is tossed six times. The probability that fewer than 2 of the tosses are heads is
a.
b.
c.
d.
e.
0.33
0.109
0.09
0.0043
none of the above
4. (6 points) In a test of ESP (extrasensory perception), the experimenter looks at cards that are hidden
from the subject. Each card contains either a star, a circle, a wavy line, or a square. An
experimenter looks at each of 100 cards in turn, and the subject tries to read the experimenter's mind
and name the shape on each. What is the probability that the subject gets more than 30 correct if the
subject does not have ESP and is just guessing?
a. 0.3100
b. 0.2500
c. 0.1251
d. less than 0.0001
e. none of the above
5. John's parents recorded his height at various ages up to 66 months. Below is a record of the results. These
results are also recorded in the exam1.MPJ
Age
(months)
Height
(inches)
36
40
48
51
54
56
60
64
66
35
36
38
40
41
42
43
45
45
a. (6 points) Find a least-squares regression line that can be used to predict John’s height using his age.
Answer: ________________________________________
b. (2 points) Use the equation found above to predict John’s height when he is 62 months.
Answer: ________________________________________
c. (5 points) Describe, using the appropriate quantifiers, the relationship John’s Age and Height share.
6. (8 points) Many test preparation companies claim to be able to increase their client’s SAT scores. Below are
the SAT scores of 40 students selected at random from a group of students who took the SAT exam twice.
The first time they took the exam was before enrolling in the test prep program and the second time was after
completing the program. The scores are arranged randomly. They can also be found in the Minitab
worksheet, exam1.MPJ.
Before
After
680
670
660
680
580
700
730
700
650
630
700
780
650
620
730
770
640
660
730
710
620
650
740
670
650
780
700
730
710
700
610
700
680
620
700
690
760
700
630
630
Use these data to assess the claims of the test prep company. Do you agree or disagree with the company’s
claim? Support your opinion statistically.
7. Based upon 1997 figures, the following are 110 “waiting times” (in minutes) between eruptions of the Old
Faithful Geyser in Yellowstone National Park. These times are also recorded in the Minitab worksheet.
81
94
91
76
91
53
82
74
83
89
80
69
83
83
89
98
94
35
83
78
67
62
76
94
73
80
91
42
85
107
55
82
78
74
89
76
60
60
98
82
94
91
82
82
65
85
74
73
89
118
82
69
69
89
89
83
105
60
82
92
98
112
80
64
73
65
40
69
80
82
56
69
82
71
87
85
83
85
94
80
60
80
98
51
78
73
83
69
71
91
67
73
33
82
78
73
73
73
74
87
65
74
74
108
87
83
73
67
64
80
a. (7 points) Describe these data. Include any and all numerical or graphical summaries you feel are appropriate.
DO NOT simply list a series of numbers. Explain your findings using complete English sentences (which
may contain numbers, symbols, etc.).
b. (3 points) Suppose that the 111th waiting time was 50 minutes. Is this data point an outlier? Briefly justify
your answer.