Math 182 Final (HH) Name ____________________________.docx

Math 182 Final (HH) Name:
________________________________
Due by Tuesday 6/9 at 11:55 PM and completed exams should
be mailed to
[email protected]
Show all work (when possible) for full credit! Ample spacing
to do the work and
give the answers has been provided for each problem, but if you
find it absolutely
necessary to use additional page(s) for work, please attach it as
the page(s)
immediately following the problem(s) that it corresponds to. It
is expected that you
will use the table in the textbook to find the probabilities for the
specific z-values
for any problems using a normal distribution.

2 3 4 5 6 7 8 9 10 Total
Points
Possible 12 8 8 16 4 8 16 8 16 4 100
Points
Scored
1) Decks of Pinochle cards have a total of 48 cards and consist
of 6 cards each of nines, tens, jacks, queens,
kings, and aces with there being two of each suit of each
denomination (for example, there are 2 aces each of
diamonds, clubs, hearts, and spades for the total of 8 aces).
Suppose that you are dealt a 8-card hand from a
deck of Pinochle cards. What is the probability that:
a) you are dealt at most 2 clubs?

b) you are dealt exactly 3 queens?
2) Suppose that you roll a pair of 16-sided dice (with the sides
numbered 1-16) a total of 125 times. What is
the probability that you will get a sum of 30 at least two times?

3) A mall has three department stores, J C Penney, Macy’s, and
Sears. A survey of 2,800 people exiting the
mall found that 513 made a purchase at J C Penney, 658 made a
purchase at Macy’s, 710 made a purchase at
Sears, 134 made a purchase at J C Penney and Macy’s, 203
made a purchase at J C Penney and Sears, 297 of
them made a purchase at Macy’s and Sears, and 82 of them
made a purchase at all three stores.
a) How many people made a purchase at Sears but did not
make a purchase at Macy’s?

b) How many people made a purchase at exactly one of the
three stores?
4) Based upon statistical studies it has been found that 3.36%
of all births in the United States will result in
twins being born. If 32,300 births are selected at random what
is the probability that:

a) between 1,000 and 1,100 of them (inclusive) will result in
twins being born?
b) at most 1,125 of them will result in twins being born?
5) Suppose an unfair coin comes up heads 39.1% of the time if
it is flipped. If the coin is flipped 11 times,
what is the probability that:
a) it comes up heads exactly 4 times?

b) it comes up tails more than 9 times?
6) The weights of full-grown male wolverines are known to be
normally distributed with a mean of 50 pounds
and a standard deviation of 7 pounds. What is the probability
that a randomly selected full-grown male
wolverine will:
a) be at least 40 pounds?
b) be less than 35 pounds or more than 70 pounds?

7) The number of home runs hit by each of the 16 regular first
basemen during the 1940 Major League baseball
season is given in the following table (regular is being defined
as the player that started the most games at first
base for each team that season):
a) Find the range, mean, median, and mode of the data set
Player Team Home Runs
Jimmie Foxx BOS (AL) 36
Buddy Hassett BOS (NL) 0

Dolph Camilli BRK (NL) 23
Joe Kuhel CHI (AL) 27
Rip Russell CHI (NL) 5
Frank McCormick CIN (NL) 19
Hal Trosky CLE (AL) 25
Rudy York DET (AL) 33
Babe Dahlgren NY (AL) 12
Babe Young NY (NL) 17
Dick Siebert PHL (AL) 5
Art Mahan PHL (NL) 2
Elbie Fletcher PIT (NL) 16
George McQuinn STL (AL) 16
Johnny Mize STL (NL) 43
Zeke Bonura WAS (AL) 3
Continued from previous page…..
7b) What proportion of the data is within 1 standard deviation
of the sample mean?

c) Construct a histogram using classes of size 8 using 0 as the
minimum possible value.

8) Suppose that a tribal culture is discovered in the South
Pacific whose language consists of only twelve
letters, A, E, G, H, I, K, L, M, O, P, T, and U. Assuming that
all possible arrangements of these letters could be
words:
a) What is the maximum possible number of 7-letter words that
this tribe can have?
b) How many 9-letter words can the tribe have that start with a
H, end with an A, and contain no T’s?
c) How many 14-letter words can the tribe have that contain

exactly 1 K, 5 A’s, 4 H’s, and 4 M’s?
d) What is the maximum possible number of 8-letter words the
tribe can have in which no letters are
repeated?
9) Three marbles are chosen without replacement from a box
containing 9 red, 4 blue, and 11 yellow marbles.
Let X be the number of red marbles chosen.
a) Find and graph the probability distribution of X.

b) Find the mean of the random variable X.

10) Suppose that you select 3 cards without replacement from a
standard deck of 52 playing cards.
a) If the first card that you select is a seven and the second is a
queen, what is the probability that the
third card that you select is a seven?
b) If the first card that you select is a ten, what is the
probability that the second card that you
select is a diamond?
11) Suppose that there are a total of 18 students in an
elementary school class. The teacher assigns each of the
students a report on a mainland country in either North America
or South America (not including the United
States) and each student is assigned a different country. The
North American countries that the teacher has to
pick from are Belize, Canada, Costa Rica, El Salvador,
Guatemala, Honduras, Mexico, Nicaragua, and Panama

(for a total of 9 countries) and the South American countries
they have to pick from are Argentina, Bolivia,
Brazil, Chile, Colombia, Ecuador, French Guiana, Guyana,
Paraguay, Peru, Suriname, Uruguay, and Venezuela
(for a total of 13 countries). Assuming that the order in which
the countries are assigned doesn’t matter:
a) In how many ways can the countries be assigned so that all
of the South American countries are
assigned?
b) In how many ways can the countries be assigned so that
there is at least one North American that is
not assigned and at least one South American country that is
not assigned?
12) A company that produces a particular machine component
has 3 factories, one each in Buffalo, Dayton, and
Pittsburgh. 32% of the components produced come from the
Buffalo factory, 39% of the components come
from the Dayton factory, and 29% of the components come from
the Pittsburgh factory. It is known that 1.2%

of the components from the Buffalo factory, 1.6% of the
components from the Dayton factory, and 1.5% of the
components from the Pittsburgh factory are defective. Given
that a component is selected at random and is
found to be defective, what is the probability that the
component was made in Buffalo?
MATH 182 Final HH

Math 182 Final (HH) Name ____________________________.docx

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