Mathematics for Practical Applications - Baseball
Exam File - Spring 2011
Exam #1
In exercises #1 - 5, a statement is given. For each exercise, identify one AND ONLY
ONE of our fallacies that is exhibited in that statement. GIVE A DETAILED
EXPLANATION TO JUSTIFY YOUR CHOICE.
1.)
2.)
3.)
4.)
5.)
"According to Joe Shlabotnik, the manager of the Waxahachie Walnuts, you should
never call a hit and run play in the bottom of the ninth inning."
"A-Rod isn't a very good fielding shortstop. After all, in 2008, he had more
strikeouts than RBIs."
"Gosh, officer, I know I made an illegal left turn, but please don't give me a ticket.
I've had a hard day, and I was just trying to get over to my aged mother's hospital
room, and spend a few minutes with her before I report to my second full-time
minimum-wage job, which I have to have as the sole support of my thirty-seven
children and the nineteen members of my extended family who depend on me for
food and shelter."
"He's made his last five shots so he's bound to miss this one."
"Who is going to win the World Series this year, the Yankees or the Nationals?"
6.)
The area inside the base paths in baseball is a 90 foot by 90 foot square.
a.)
What is that area in acres?
b.)
What is that area converted to meters?
7.)
If Jose Reyes hits an inside the park home run, running 385 feet (the base paths
would be 360 feet but a 90 degree turn is tough) in 12.5 seconds, then what is
his average speed in miles per hour?
8.)
Suppose you went back in time 1,000,000,000 (1 billion) seconds. What year
would it be?
9.)
CC Sabathia signed a contract with the New York Yankees for $161 million.
Convert the contract amount to Mexican pesos. You must show the use of
units and conversion factors.
10.)
On September 10, 1960, Mickey Mantle hit a home run against Paul Foytack that
cleared the right-field roof at Tiger Stadium. Based on where it was found, it was
later estimated to have traveled 643 feet. How many millimeters did the ball
travel? You must show the use of units and conversion factors.
11.)
A person is interested in finding out what college football team people in the
United States like most. In order to do that, he does a survey by asking people in
Arkansas what their favorite college football team is. Are his results likely to be
representative of Americans? Why or why not?
12.)
CNN is doing a poll on their web site. Explain why this poll is biased.
13.)
For each of the following, tell whether it is an example of a qualitative statistic or a
quantitative statistic.
a.)
height of people who play baseball professionally
b.)
number of times a batter strikes out with men on base and less than two out
c.)
eye color of students at Henderson State University
d.)
percentage of freshmen students at Henderson State University who finish
with a GPA of 3.0 or higher
14.)
Name four different rule changes that we discussed from chapters 1-3 of Schwarz's
book.
15.)
Matching - For each item in Column B, place in the blank the number of the
associated name from Column A. Note that there are more choices in Column A
than in Column B. No answer should be used more than once.
Column A
1.)
1869 Cincinnati Red
Stockings
2.)
1884 Troy Trojans
3.)
Alan Roth
4.)
Albert Spalding
5.)
Art Richmond
6.)
Babe Ruth
7.)
Bill James
8.)
Bill Veeck
9.)
Branch Rickey
10.)
Henry Chadwick
11.)
John Heydler
12.)
John Lawres
13.)
Lee Allen
14.)
Richie Ashburn
Column B
________
________
________
________
________
________
________
________
________
________
"The Father of Baseball"
began collecting players' lifetime
statistics that were not available
anywhere, eventually publishing a
book, Who's Who in Baseball, in 1912
hired the first full-time statistician
In 1977, he published his first Abstract,
giving statistics along with analysis and
commentary. According to Schwarz,
he did more than anyone else to
popularize the study of baseball
statistics and analysis.
National League secretary and
statistics fanatic, particularly pitching
statistics
star pitcher, manager, helped form
National League in 1876, started
sporting goods company
the appeal of his home runs led
baseball to try to help increase power
hitting
the first openly professional team
was hired as first full-time statistician
Was the preeminent baseball historian
of the era of the 20th century
Exam #2
1.)
The following chart shows the National League leaders in home runs from 1965.
Draw a bar graph to illustrate the data.
Name
HR
Billy Williams
34
Frank Robinson
33
Ron Santo
33
Willie Mays
52
Willie McCovey
39
2.)
The following chart shows Willie Mays' double, triple, home run and stolen base
totals from 1954-1962.
a.)
3.)
In which year (from 1954-1962) did Mays hit the most home runs? How
many did he hit that year?
b.)
How many times (from 1954-1962) did Mays have more stolen bases than
home runs?
c.)
Did Mays ever have a year in which he had at least 20 doubles, triples,
home runs and stolen bases in the same year (from 1954-1962)? If so,
which year?
d.)
How many home runs did Willie McCovey hit in 1961?
e.)
How many extra base hits (doubles, triples and home runs) did Mays have in
1958?
The following chart shows the number of wins for pitchers on the 1986 Mets.
a.)
b.)
c.)
d.)
e.)
4.)
If the team won 108 games and Dwight Gooden won 17, what is the angle
for his piece of the pie?
Five pitchers won more than ten games for the 1986 Mets. Who were they?
How many pitchers won games for the 1986 Mets?
The angle for Bob Ojeda's piece of the pie is 60. How many games did he
win?
Who won more games, Roger McDowell or Jesse Orosco for the 1986
Mets?
The following shows some career statistics for Rogers Hornsby.
YEAR
1915
1916
1917
1918
1919
1920
1921
1922
1923
1924
1925
1926
1927
1928
1929
1930
1931
1932
1933
1934
1935
1936
1937
TOTALS
AB
57
495
523
416
512
589
592
623
424
536
504
527
568
486
602
104
357
58
92
23
24
5
56
8173
R
5
63
86
51
68
96
131
141
89
121
133
96
133
99
156
15
64
10
11
2
1
1
7
1579
H
14
155
171
117
163
218
235
250
163
227
203
167
205
188
229
32
118
13
30
7
5
2
18
2930
2B
2
17
24
19
15
44
44
46
32
43
41
34
32
42
47
5
37
2
7
2
3
0
3
541
3B
0
15
17
11
9
20
18
14
10
14
10
5
9
7
8
1
1
0
0
0
0
0
0
169
HR
0
6
8
5
8
9
21
42
17
25
39
11
26
21
39
2
16
1
3
1
0
0
1
301
RBI
4
65
66
60
71
94
126
152
83
94
143
93
125
94
149
18
90
7
23
11
3
2
11
1584
AVG
.246
.313
.327
.281
.318
.370
.397
.401
.384
.424
.403
.317
.361
.387
.380
.308
.331
.224
.326
.304
.208
.400
.321
.358
SLG
.281
.444
.484
.416
.430
.559
.639
.722
.627
.696
.756
.463
.586
.632
.679
.433
.574
.310
.500
.522
.333
.400
.429
.577
OBA
.271
.369
.385
.349
.384
.431
.458
.459
.459
.507
.489
.388
.448
.498
.459
.385
.421
.357
.426
.484
.296
.500
.397
.434
OPS
.552
.814
.868
.764
.814
.990
1.097
1.181
1.086
1.203
1.245
.851
1.035
1.130
1.139
.817
.996
.667
.926
1.006
.630
.900
.825
1.010
a.)
b.)
c.)
d.)
In how many years did Hornsby have a batting average (AVG) of at least
.400?
In how many seasons did Hornsby exceed 100 in BOTH runs (R) and runs
batted in (RBI)?
What is the most home runs Hornsby ever hit in one season? What year?
How many runs did Joe Medwick score in 1934?
5.)
A jacket is priced at $180. It goes on sale for 15% off. A week later it is reduced
another 10%. What is the price now?
6.)
A jacket is on sale at 15% off. The price of the jacket is now $340. What was
the original price?
7.)
The following data are the number of doubles for Bob "Death to Flying Things"
Ferguson from 1873 through 1878. WITHOUT USING YOUR CALCULATOR
AT ALL, find the following. BE SURE TO SHOW ALL WORK FOR FINDING
THE ANSWERS.
3
4
10
8
7
10
a.)
mean
b.)
median
c.)
mode
8.)
Through 2008, Mark Teixeira had 203 career home runs. For his career, Robin
Yount had 251 home runs. For his career, Gavvy Cravath had 119 home runs.
Explain (giving at least two reasons) why we cannot conclude anything about
which of these players was the best home run hitter based on the information
given.
9.)
The following are the major league leaders in Innings Pitched from 1962.
Art Mahaffey
274
Jim Bunning
258
Bill Monbouquette
235
Jim Kaat
269
Billy O'Dell
281
Jim O'Toole
252
Bob Friend
262
Joey Jay
273
Bob Gibson
234
Johnny Podres
255
Bob Purkey
288
Juan Marichal
263
Camilo Pascual
258
Larry Jackson
252
Dick Donovan
251
Ralph Terry
299
Don Drysdale
314
Ray Herbert
237
Ed Rakow
235
Turk Farrell
242
Gene Conley
242
Warren Spahn
269
Jack Kralick
243
Whitey Ford
258
Jack Sanford
265
Find the following: (You may use your calculator)
a.)
mean
b.)
median
c.)
mode
d.)
five number summary:
minimum, lower quartile, median, upper quartile, maximum
10.)
For each of the following sets of statistics, fill in the blanks.
1941 Ted Williams, Boston Red Sox
AB
H 2B 3B HR BB
456 185 33 3 37 147
AV
HBP
3
TB
SL
OB
ERA
SO/IP
OPS
1915 Pete Alexander, Philadelphia Phillies
W
L
31
10
PCT
IP
H
ER
BB
SO
376
253
51
64
241
WHIP
1975-1976, Julius Erving, American Basketball Association, New York Nets
games
84
free
free
free
rebounds
throws
throws
throw rebounds per game
made attempted
%
530
662
925
points
points
per
game
2462
1970, Bob Hayes, National Football League, Dallas Cowboys
Receiving
Games
Receptions
Yards
13
34
889
Rushing
Yards per
Reception
Attempts
Yards
4
34
Yards per
attempt
11.)
A person is interested in finding out the average income of people in Arkansas.
In order to do that, he does a survey by asking the annual income of Arkansas
residents in line at the Reddie Café in the Garrison Center. Are his results likely
to be representative of Arkansas? Why or why not?
12.)
The following is information about the players who played at least 100 games at
third base in the 1964 National League. Which one would you choose as the most
valuable third baseman. Explain your reasoning.
Bob Aspromonte
Bob Bailey
Dick Allen
Eddie Mathews
Jim Ray Hart
Ken Boyer
Ron Santo
Steve Boros
AVG HR RBI
OBA
.280
.281
.318
.233
.286
.295
.313
.257
.329
.336
.382
.344
.342
.365
.398
.342
12
11
29
23
31
24
30
2
69
51
91
74
81
119
114
31
Fielding
PCT
.973
.943
.921
.962
.937
.951
.963
.961
Exam #3
1.)
2.)
3.)
4.)
5.)
6.)
7.)
8.)
In 1897, all three outfielders for the Phillies batted at least .400. Billy Hamilton hit
.404 and Sam Thompson and Ed Delahanty each hit .407. We will view their
batting averages as probabilities, assume that all at bats are independent events
and ignore walks, etc.
a.)
Assume that the three bat right after each other in one inning. What is the
probability that all three get hits?
b.)
Assume that the three bat right after each other in one inning. What is the
probability that all three make outs?
c.)
If what is the probability that Hamilton gets a hit but Thompson and
Delahanty make outs?
d.)
If Delahanty has two at bats, what is the probability that he gets hits both
times?
e.)
If Hamilton bats six times, what is the probability he gets at least one hit?
f.)
If Delahanty and Hamilton bat, what is the probability that one, but not
both, gets a hit?
In 1969, Tommie Agee, Cleon Jones, Ron Swoboda, Art Shamsky, Rod Gaspar,
and Amos Otis were the main outfielders for the New York Mets. We are
interested in how many different groups of outfielders they could have had.
a.)
Is this a permutations problem or a combinations problem?
b.)
How many different groups were possible?
a.)
Draw a tree diagram to illustrate the flipping of three coins.
b.)
What is the probability of having exactly 2 heads?
c.)
What is the probability of having at least 2 heads?
You are making a license plate. It has 3 letters followed by 4 numbers. How
many different license plates can be made?
In their lunch menu, the Olive Garden restaurant in Fort Smith, offers nine
appetizers, three soups, two salads, thirty-four entrees, forty-two beverages and
eight desserts. If you order one appetizer, one soup, one salad, one entrée, one
beverage and one dessert, how many different meals could you order?
A box contains 8 arthropods, 7 cephalopods and 5 paramecia. You reach into
the box and pull out a creature at random. You then pull out another creature.
What is the probability that you pull out two cephalopods?
Fifteen people have formed a baseball team. We are interested in the number of
nine player batting orders that can be created from the fifteen players.
a.)
Is this a combination problem or a permutation problem?
b.)
How many different lineups are possible?
You put $5400 in the bank. The account gets an annual percentage rate of
interest of 3.21% compounded quarterly. The money is left in the account for 4
years. No other money is added or removed from the accounts.
a.)
Without inserting any numbers, write the formula you will need for this
problem.
b.)
Without doing any simplification, insert the right numbers in the right
places in the formula.
c.)
How much money will you have at the end of four years?
9.)
The following chart gives some of Babe Ruth's career statistics.
Team
1914 Red Sox
1915 Red Sox
1916 Red Sox
1917 Red Sox
1918 Red Sox
1919 Red Sox
1920 Yankees
1921 Yankees
1922 Yankees
1923 Yankees
1924 Yankees
1925 Yankees
1926 Yankees
1927 Yankees
1928 Yankees
1929 Yankees
1930 Yankees
1931 Yankees
1932 Yankees
1933 Yankees
1934 Yankees
1935 Braves
TOTAL
a.)
10.)
11.)
AB
10
92
136
123
317
432
458
540
406
522
529
359
495
540
536
499
518
534
457
459
365
72
8,399
H
2
29
37
40
95
139
172
204
128
205
200
104
184
192
173
172
186
199
156
138
105
13
2,873
2B
1
10
5
6
26
34
36
44
24
45
39
12
30
29
29
26
28
31
13
21
17
0
506
3B
0
1
3
3
11
12
9
16
8
13
7
2
5
8
8
6
9
3
5
3
4
0
136
HR
0
4
3
2
11
29
54
59
35
41
46
25
47
60
54
46
49
46
41
34
22
6
714
If he had an at bat (AB), what was his career probability of hitting a home
run (HR)?
b.)
In 1931, if he had a hit (H), what was the probability it was a double (2B)?
You start putting money in your retirement fund at age 23. You put in $500 each
month. The interest of 10.25% is compounded quarterly. You retire at age 65.
a.)
Without inserting any numbers, write the formula you will need for this
problem.
b.)
Without doing any simplification, insert the right numbers in the right
places in the formula.
c.)
How much money will you have at age 65?
d.)
What is the total of all of your payments?
e.)
How much interest did your money earn?
Maher-Shalal-Hash-Baz started putting money in a college savings account. He
wants to have $120,000 in 18 years when his son will be ready for college. The
interest rate of 9.5% is compounded quarterly. He'll make quarterly payments.
a.)
Without inserting any numbers, write the formula you will need for this
problem.
b.)
Without doing any simplification, insert the right numbers in the right
places in the formula.
c.)
How much money will he have to pay each quarter?
d.)
What is the total of all of his payments?
e.)
How much interest did his money earn?
12.)
You are buying a house. After the down payment, you need to borrow $115,000.
You will take out a mortgage to cover the remaining cost of the house. The interest
rate for your 30 year mortgage is 6.15%.
a.)
Without inserting any numbers, write the formula you will need for this
problem.
b.)
Without doing any simplification, insert the right numbers in the right
places in the formula.
c.)
What will be your monthly payment?
d.)
What will be the total of all of your monthly payments?
e.)
How much interest will you pay over the life of the loan?
Exam #4
1.)
Find the area and perimeter of the following figure. All measurements are in feet.
2.)
The window below is shaped like a rectangle with a semi-circle on top. What are
the area and perimeter of the window? Give at least 4 places to the right of the
decimal point.
3.)
A cylindrical storage drum has a height of 2 feet and a diameter of one yard.
Find the volume and surface area. Give at least 4 places to the right of the
decimal point.
In 1985, the highest paid major league baseball player made $2,130,300. In
1986, the highest paid player earned $2,800,000. That was an increase of
31.4369%. If salaries continued to grow exponentially at that rate, what would
the highest paid player have earned in 2005? (The highest paid player in 2005
made $26,000,000.)
4.)
5.)
Below is the 1923 baseball design of the Polo Grounds in New York City.
Approximate the area (in acres) of fair territory. BE SURE TO SHOW
ALL OF YOUR WORK.
6.)
Suppose a ball is hit from a height of 4 feet with a velocity of 79 miles per hour
(115.8667 feet per second) at an angle of elevation of 43. Find the following.
[Put your calculator in PAR mode and use the following equations in the y=
window.]
x = v0 (cos ) t
y = -16t2 +v0 (sin ) t + y0
a.)
how far it travels
b.)
how long it takes to land
c.)
if it is a home run over an 8 foot tall fence at 400 feet (explain the
reasoning for your answer)
7.)
Find the volume and surface area of the box shown below. Assume all
measurements are in feet.
8.)
9.)
10.)
Find the area and perimeter of circle with radius 8 inches. Give your answer to at
least four decimal places.
A conical container has a height of 2 feet and a diameter of one yard. Find the
volume and surface area. Give at least 4 places to the right of the decimal point.
Suppose a ball is dropped from a height of 75 feet. Use your calculator to
determine how long it will take for it to hit the ground. [Put your calculator back in
FUNC mode and use y = -16x2 + 75 in your Y= window.]
Final Exam
In exercises #1 - 3, a statement is given. For each exercise, identify one AND ONLY
ONE of our fallacies that is exhibited in that statement. GIVE A DETAILED
EXPLANATION TO JUSTIFY YOUR CHOICE.
1.)
2.)
3.)
4.)
5.)
6.)
7.)
8.)
9.)
Former major league pitcher Ross Grimsley, nicknamed "Scuzz," would not wash
or change any part of his uniform as long as the team was winning, believing that
washing or changing anything would jinx the team.
"Buy new and improved CRUST™ toothpaste, the toothpaste used by more
people than any toothpaste in the country!"
"Eighty year old people don't need to go into nursing homes. After all my mother
is 85 and she power-walks two miles each day, drives her car (safely), climbs
stairs, does crosswords, and reads the daily paper." (adapted from http://www.fallacyfiles.org)
Walter Young, at 322-pounds, is believed to be the heaviest major league
baseball player ever. Convert his weight to kilograms.
Tom threw a baseball 44.7 meters per second. Dave threw a ball 92 miles per
hour. Who threw the ball faster, Tom or Dave? Be sure to show all necessary
work.
The price of a sofa was $800. Two weeks ago the price was dropped 15%. This
week it was dropped 10%. What is the price now?
David Wright, of the New York Mets, earned $374,000 in 2006. That was a raise
of 15.969% from his 2005 salary. What was his 2005 salary?
Bubba's yard measures 200 meters by 300 meters. How many acres is that?
In 1957, Frank Robinson had 611 at bats, 197 hits and 29 home runs.
a.)
What was his batting average?
b.)
What percentage of his hits were home runs?
10.)
The following are some of the career statistics for Hall of Fame pitcher Warren
Spahn.
Year
Team
G
W
IP
H
BB
SO
1942 Braves
4
0
0 .000 5.74
1
0
15.2
25
10
0
11
7
1946 Braves
24
8
5 .615 2.94
8
0
125.2
107
41
6
36
67
1947 Braves
40
21
10 .677 2.33
22
7
289.2
245
75
15
84
123
1948 Braves
36
15
12 .556 3.71
16
3
257.0
237
106
19
77
114
1949 Braves
38
21
14 .600 3.07
25
4
302.1
283
103
27
86
151
1950 Braves
41
21
17 .553 3.16
25
1
293.0
248
103
22
111
191
1951 Braves
39
22
14 .611 2.98
26
7
310.2
278
103
20
109
164
1952 Braves
40
14
19 .424 2.98
19
5
290.0
263
96
19
73
183
1953 Braves
35
23
7 .767 2.10
24
5
265.2
211
62
14
70
148
1954 Braves
39
21
12 .636 3.14
23
1
283.1
262
99
24
86
136
1955 Braves
39
17
14 .548 3.26
16
1
245.2
249
89
25
65
110
1956 Braves
39
20
11 .645 2.78
20
3
281.1
249
87
25
52
128
1957 Braves
39
21
11 .656 2.69
18
4
271.0
241
81
23
78
111
1958 Braves
38
22
11 .667 3.07
23
2
290.0
257
99
29
76
150
1959 Braves
40
21
15 .583 2.96
21
4
292.0
282
96
21
70
143
1960 Braves
40
21
10 .677 3.50
18
4
267.2
254
104
24
74
154
1961 Braves
38
21
13 .618 3.02
21
4
262.2
236
88
24
64
115
1962 Braves
34
18
14 .563 3.04
22
0
269.1
248
91
25
55
118
1963 Braves
33
23
7 .767 2.60
22
7
259.2
241
75
23
49
102
1964 Braves
38
6
13 .316 5.29
4
1
173.2
204
102
23
52
78
1965 Mets/Giants
36
7
16 .304 4.01
8
0
197.2
210
88
26
56
90
21 Years
a.)
11.)
L PCT ERA CG SHO
750 363 245 .597 3.09 382
ER HR
63 5,243.2 4,830 1,798 434 1,434 2,583
How many times did Warren Spahn allow more than 20 home runs (denoted
HR)?
b.)
What is the most consecutive years Warren Spahn won at least 20 games
(denoted W)?
c.)
What was the lowest earned run average (denoted ERA) that Warren Spahn
had in a year in which he had at least 275 innings pitched (denoted IP)?
d.)
What was the most wins Lew Burdette had in a single year?
You put $3200 in a certificate of deposit account. It receives 3.25% interest
compounded quarterly. You neither take out any money nor put in any more
money.
a.)
Write out the formula that will figure out the amount of money you will
have after 3 years without any of the numbers inserted.
b.)
Write out the formula that will figure out the amount of money you will
have after 3 years with all of the numbers inserted.
c.)
How much money will you have after 3 years?
12.)
You start putting money in your retirement fund at age 27. You put in $900 each
quarter. The interest of 10.16% is compounded quarterly.
a.)
Without inserting any numbers, write out the formula that will figure out the
amount of money you will have if you retire at age 62.
b.)
Without doing any simplification, insert all of the numbers into the formula.
c.)
How much money will you have at age 62?
d.)
What is the total of all of your payments?
13.)
The following chart shows all men who had at least 30 home runs in the National
League in 1957. In the chart, "2B" stands for "doubles," "3B" stands for "triples"
and "HR" stands for "Home Runs." Answer the following questions.
a.)
b.)
c.)
d.)
Of these players, who had the most triples in 1957? How many?
Who had the most doubles in the National League in 1957?
How many of these players had more than 25 doubles in 1957?
"Extra Base Hits" would be the sum of a player's doubles, triples and home
runs. Of these players, who had the most extra base hits in 1957?
14.)
Bubba is borrowing $34,000 to buy a new double-wide. The interest rate for his 15
year mortgage is 7.85%. Throughout the problem we will ignore the escrow
payments that would normally be added to the mortgage payment to cover
insurance and taxes.
a.)
Without inserting any numbers, write out the formula that will figure out the
amount of Bubba's monthly payments.
b.)
Without doing any simplification, insert all of the numbers into the formula.
c.)
What will be his monthly payment?
d.)
What will be the total of all of his monthly payments?
e.)
How much interest will he pay over the life of the loan?
15.)
Johan Santana (pitcher), Ramon Castro (catcher), Carlos Delgado (first base),
Luis Castillo (second base), Jose Reyes (shortstop), David Wright (third base),
Daniel Murphy (left field), Carlos Beltran (center field) and Ryan Church (right
field) will be playing for the Mets. With the restrictions that Santana will bat 9th
and Reyes will bat 1st, how many different batting orders are possible.
16.)
The following chart shows percentage distribution of pitching wins for the 1966 Los
Angeles Dodgers. The team won 95 games. [Note: It is not possible to have a
fractional win so round off any answers that ask for a number of wins.]
a.)
b.)
c.)
d.)
Who had the most wins for the 1966 Dodgers?
How many pitchers had wins for the 1966 Dodgers?
How many games did Don Drysdale win?
What is the angle for Claude Osteen's piece of the pie?
17.)
A cylindrical storage drum has a height of 4 feet and a diameter of two yards.
Find the volume and surface area. GIVE AT LEAST 4 PLACES TO THE RIGHT
OF THE DECIMAL POINT!!
18.)
In 1897, all three outfielders for the Phillies batted at least .400. Billy Hamilton hit
.404 and Sam Thompson and Ed Delahanty each hit .407. We will view their
batting averages as probabilities, assume that all at bats are independent events
and ignore walks, etc.
a.)
Assume that the three bat right after each other in one inning. What is the
probability that all three get hits?
b.)
Assume that the three bat right after each other in one inning. What is the
probability that all three make outs?
c.)
Assume that the three bat right after each other in one inning. What is the
probability that Hamilton gets a hit but Thompson and Delahanty make
outs?
d.)
If Delahanty has two at bats, what is the probability that he gets hits both
times?
19.)
The following are the numbers of times Hall of Famer Earl Averill was hit by pitches
(denoted HBP) in his first six seasons in the major leagues. Find the following
WITHOUT USING YOUR CALCULATOR AT ALL AND YOU MUST GIVE SOME
INDICATION OF HOW YOU FOUND THE NUMBER.
Year
1929
1930
1931
1932
1933
1934
HBP
3
2
6
6
5
4
a.)
b.)
c.)
d.)
mean
median
mode
minimum
For each of the following sets of statistics, fill in the blanks.
20.) 1941 Ted Williams, Boston Red Sox
AB
H 2B 3B HR BB AV HBP SF TB
456 185 33 3 37 147
3
0
21.)
22.)
SL
OB
OPS
1915 Pete Alexander, Philadelphia Phillies
W
L
31
10
PCT
IP
H
ER
BB
SO
376
253
51
64
241
ERA
SO/IP
WHIP
The following were the major league leaders in total bases in 1932. Find the
following.
Name
Total Bases
Name
Total Bases
Earl Averill
359
Smead Jolley
273
Wally Berger
282
Chuck Klein
420
Jack Burns
270
Hal Lee
296
Bruce Campbell
273
Heinie Manush
325
Ben Chapman
275
Lefty O'Doul
330
Earle Combs
269
Mel Ott
340
Joe Cronin
274
Babe Ruth
302
Jimmie Foxx
438
Al Simmons
367
Lou Gehrig
370
John Stone
283
Charlie Gehringer
307
Bill Terry
373
Babe Herman
312
Joe Vosmik
287
Don Hurst
317
Paul Waner
321
Pinky Whitney
280
a.)
b.)
c.)
d.)
mean
median
mode
maximum
23.)
Find the area and perimeter for the following parallelogram.
24.)
Mineral Springs, Arkansas had a population of 546 in 1880. By 1900, it had lost
half of its population. Assuming the population continued to decline exponentially
at the same rate, what would the population be in 2005? (Note: the actual 2000
population was 1,264.)
25.)
You roll two dice. What is the probability that the sum of the numbers on the
dice is greater than 9?