Test 3 August 1, 2003 Name This is a take home test ...

Test 3 August 1, 2003 Name

Math 109 Student Number

Direction: This is a take home test. Please drop this test in my mailbox in room
328 of Natural Sciences Building on Friday (August 1, 2003) on or before 10:00
AM. You should do the test by yourself. In order to receive full credit, answer
each problem completely and must show all work. Good luck!

1. (25 points) A coin will be tossed 1000 times and the quantity, “five times the number of
heads minus the twice number of tails” is computed. What is the appropriate box model?

2. (25 points) A coin will be tossed 500 times and the quantity, “the number of heads plus
the twice number of tails” is computed. What is the appropriate box model?

3. (30 points) One hundred draws will be made at random with replacement from the box:

1 6 7 9 9 10

(a) (3 points) How small can the sum of these 100 draws be?
(b) (3 points) How large can the sum of these 100 draws be?
(c) (11 points) What is the EV for the sum of these 100 draws?

(d) (13 points) What is the SE for the sum of these 100 draws?

4. (20 points) One hundred draws will be made at random with replacement from the box:

1 6 7 9 9 10

What is the chance that the sum of these 100 draws is a number between 650 and 750?

5. (30 points) Four hundred draws will be made at random with replacement from the box:

-1 -2 0 1 3

(a) (3 points) How small can the sum of these 400 draws be?
(b) (3 points) How large can the sum of these 400 draws be?
(c) (10 points) What is the EV for the sum of these 400 draws?

(d) (14 points) What is the SE for the sum of these 400 draws?

6. (20 points) One hundred draws will be made at random with replacement from the box:

-1 -2 0 1 3

What is the chance of getting between 14 and 28 tickets marked 3?

7. (25 points) You play roulette 400 times betting $100 on number 13 each time. The bet
pays 35 to 1, and you have 1 chance in 38 to win. What is your chance of coming out ahead?

8. (25 points) Consider the sum of 25 draws with replacement from the box:

0 2 3 46

The chance experiment for determining the sum is repeated a number of times. One of the
following is the sequence of observed values. Which one (and you must explain why)?

(A) 76, 84, 95, 85, 100, 70, 91, 103, 68, 97
(B) 75, 76, 74, 76, 77, 73, 75, 72, 74, 76
(C) 50, 100, 97, 104, 58, 71, 83, 112, 49, 65
(D) 84, 70, 91, 80, 74, 50, 65, 82, 88, 81

9. (25 points) A coin will be tossed 400 times. Estimate the chance of getting
(a) exactly 210 heads.

(b) between 180 and 240 heads inclusive.

(c) between 180 and 240 heads exclusive.

10. (25 points) Define the following terminologies:
(a) population
(b) sample
(c) statistical inference
(d) simple random sample
(e) quota sampling

The final examination will be held on August 8 at 9:40 AM