math

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.

Page 1 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?