A.P. Statistics Summer Assignment

Welcome to AP Statistics. The course is built around four main topics; exploring data, planning a study, probability as it relates to distribution of data and inferential reasoning. Among leaders of industry, business, government, and education, almost everyone agrees that some knowledge of statistics is necessary to be an informed citizen or a productive worker. Statistics are often used to influence consumers or to back public opinions. Quantitative information is the basis for decision-making in almost every job. This assignment is due the FIRST day of class and will count as your first test grade (90 points) . The packet contains seven (7) sections. Sections I through V and VII contain definitions, examples, solutions and problem sets. Section VI is a basic math skills sections. These questions review concepts that all AP Statistics students should know before entering the class. You will find an answer key at the end of the packet. (Please write all your answers on the answer keys.) Make sure that you read all directions. Some sections of the packet will be done in class the first week and you are not responsible for them over the summer. These sections are clearly marked. Summer Packet Guidelines

• Start summer assignment early to allow for time to complete it • If you can not complete problems on your own, you may use math reference

sheets, books, websites, and/or your notes to find the solutions • You well be assessed on both your answer and your work. Attach ALL work with

your packet. If you simply hand in answers, you will receive no credit!! • Complete ALL problems in the packet except those that are clearly labeled. • If you have any questions will you are working, please feel free to email me at

kavcakc@warrenhills.org. NOTE: A summer assignment NOT received on the first day of class will not be accepted. Students not submitting the work on the first day will receive will receive a ZERO.

DO NOT HAVE TO DO

Show your strategy.

DO NOT HAVE TO DO (6-8)

VII. Combinations and Permutations Counting Principle: The computation of theoretical probabilities is based upon an important counting principle called logical multiplication.

• If a person has 3 different sweatshirts and 2 different pairs of jeans, then there are

!

3•2 = 6 possible outfits. • If there is a family of 6 children, and assuming both genders are equally likely at

birth, how many different gender arrangements are there? For each child, there are 2 possibilities (B or G) and each birth is independent of the others, therefore

!

26

= 64 possible arrangements. • How many ways are there of arranging 5 children to stand in a line? For the first

space, there are 5 choices, for the next space, 4 choices, and so on until the last space when there is only one choice, the last child. The total number of ways is

!

5• 4 • 3•2•1= 5!=120 Permutations: an arrangement, which ORDER MATTERS

• In how many different ways can we pick a 4 letter “word” from the word MATH? As explained above, the answer would be 4! = 24 ways.

• In how many ways a 7 letter “word” from the letters ENGLAND? If all the letters were different, there would 7! Ways. However, there are 2 N’s and so there

would be half as many

!

7!

2!

"

# $

%

& ' ways. Similarly, there are

!

9!

2!•2!

"

# $

%

& ' way of getting a

word from the letters JEFFERSON • In how many ways can we arrange the 4 letters from a total of 6 letters? Using

the counting principle, we can see that it would be

!

6•5• 4 • 3 =6!

2!=

6!

(6 " 4)!. In

general, the number of different permutations of n items taken r items at a time is

denoted by

!

nPr

=n!

(n " r)!

Combinations: an arrangement, which ORDER DOES NOT MATTER 1. There is only 1 way to choose 3 letters from CAT because CAT is considered the

same choice as CTA, TCA, TAC, ACT, and ATC. There are FEWER ways of arranging items then when order matters.

2. In general, the number of ways that r items can be chosen from n elements is

!

nCr

=n!

r!(n " r)!

Problem Set VII Counting Principle

1. If a sandwich shop has 3 different types of meat, 4 types of bread, and 3 different types of cheese. How many types of sandwiches can you create if you must have one meat, one bread and one cheese on each?

2. How many ways can you hang 3 pictures in a row on a wall?

3. How many ways can you visit 5 exclusive shops when you are looking for the perfect present for your best friend?

4. If a person has 4 pairs of shoes and 6 pairs of socks, then how many shoe-sock combos are possible?

5. If there is a family of four, how many different gender arrangements are there?

6. If you are taking a multiple-choice test (a, b, c, and d) consisting of 10 questions, then how many different arrangements of answers are there?

Permutations (Key word: arrange)

7. How many ways can you pick a 6 letter “words” from the word STREAK?

8. How many ways can we pick a 10 letter “words” from the word STATISTICS?

9. How many ways can we pick 3 different club officers from a club of 20 members?

Combinations (key word: select)

10.

!

5C3

=

!

7C4

=

!

10C3

=

11. How many ways can we select a committee of 3 people from a club of 20 members?

12. How many ways can we pick 4 winners for 8 prizes if each is the same?

Problem Set VI (32 points) Problem Set VII (12 points) 1) __________ 14) __________ 1) __________ 2) __________ 18) __________ 2) __________ 3) __________ 19) __________ 3) __________ 4) __________ 20) __________ 4) __________ 5) __________ 21) __________ 5) __________ 6) __________ 22) __________ 6) __________ 7) __________ 23) __________ 7) __________ 8) __________ 24) __________ 8) __________ 9) __________ 25) __________ 9) __________ 10) __________ 26) __________ 10) __________ 11) __________ 27) __________ 11) __________ 12) __________ 28) __________ 12) __________ 13) __________ 29) __________ 14) __________ 30) __________ 15) __________ 31) __________ 16) __________ 32) __________