Diagnostic Exam

This diagnostic exam is to help both you and us. You should find all of these problems straightforward. Please do not use a calculator -- in many cases an estimate will be plenty.

Your score on this quiz will not affect your grade, but please do your best. The only person who is evaluating your performance on this is you.

This section, where you identify yourself, is optional. Anyone can take this exam.
Name:   Last First
Major?
(undecided is OK) 		Graduation Year
 
Any previous statistics course? What?
Computer programming experience? What?

Below, if you do not know the answer to a question, do not guess -- just leave it blank. For some problems, answer Can't tell if you need more information to answer the question.

1. 300 is what percent of 2,000?

.67% 1.5% 6.7% 15% 33% Can't tell

 

2. A town has 100,000 families. One tenth of one percent of these families have incomes over $75,000 a year. The number of such families is

1 10 100 1,000 1,500 Can't tell

 

3. There are 100 million eligible voters in the United States. The Gallup pole interviews 5,000 of them. This amounts to 1 eligible voter out of every   ?   voters.

200 2,000 5,000 20,000 50,000 Can't tell

 

4. In the United States, 1 person out of every 500 is in the army, and 3 out of every 10,000 Americans are army officers. What percentage of army personnel are officers?

.15% .2% 5% 15% 20% Can't tell.

 

5. In the United States, 1 person out of every 2,000 is a marine, and one-tenth of marine personnel are officers. What percentage of the U.S. Population consists of marine officers?

.002% .005% .02% .05% .2% Can't tell

 

6. is about

300 400 500 1,000 3,000 Can't tell

 

7. .

True False Don't know

 

8. is smaller than .5 .

True False Don't know

 

9.

True False Don't know

 

10. A quart of vodka is 40% alcohol. Write a formula for the percentage of alcohol in a mixture of   V   quarts of vodka and   J   quarts of orange juice.


.4V
40V/(V + J)
(4V + J)/(V + J)
(40V + J)/(100 J)
.40V/ J

 

11. This year John's mother is exactly three times as old as he is. Next year their ages will add up to 50. How old is John?

5 6 12 15 24 Can't tell

 

12. Here is a quadratic equation:   3x2 + 17x -28.9207 = 0. One of the following is a solution; which one?

0.1 0.87 1.37 2.17 3.81

 

13. The graph of the equation   y = (1/3)x + 2   is a straight line. Does the point (5.1, 3.5) lie on the line?

Yes No Need more information.

 

14. You throw one die. What is the chance of getting an ace ?

1/12 1/6 1/4 1/3 1/2 Can't tell

 

15. You throw a pair of dice. What is the chance of getting two
aces: ?

1/72 1/36 1/24 1/18 1/12 Can't tell

 

16. Here are three situations:
    (i) A coin will be tossed 100 times. If it comes up heads 60 or more times you win $2.
    (ii) A coin will be tossed 1,000 times. If it comes up heads 600 or more times you win $2.
    (iii) A (fair) coin has been tossed 100 times and 73 have been tails. If it comes up heads at least 60 times in the next 100 tosses you win $2.
Which is better -- or do they offer the same chance of winning?

(i) (ii) (iii) Same chance.

 

The next three questions refer to the histogram below.
A group of people were asked how many hats they own. This summarizes their replies. The horizontal axis is the number of hats, so min = 0, max = 5, while the vertical axis is the number of people who gave that reply.

17. How many people replied?

5 6 8
10 20 Can't tell

 

18. What was the mean reply?

3 3.3 3.5
3.7 4 Can't tell

 

19. median ?

3 3.3 3.5 3.7 4 Can't tell

 

20. The derivative of   x2   is  

2 2x 2x + C x/2 + C x Can't tell

 

21. =

11/4 3 13/4 15/4 4 Can't tell

 

22. If  dy/dx  =  x  with  y(0) = 3,  then   y(2) =  

5/2 4 5 6 7

 

23. To find the value of   c   that minimizes

Differentiate with respect to   x
Differentiate with respect to   c
Can't do it by calculus.

 

The next two problems refer to the graph of   h(x)   on the right.

24. Which of the following best describe the graph at P? (here   h'  is the first derivative and   h''  the second).
  h'>0,  h''<0   h'>0,  h''>0   h'=0,  h''<0
  h'=0,  h''>0   h'<0,  h''>0   h'<0,  h''<0

 

25. Which of the following best describe the graph at Q?
  h'>0,  h''<0   h'>0,  h''>0   h'=0,  h''<0
  h'=0,  h''=0   h'<0,  h''>0   h'<0,  h''<0

 

A-1. I know how to make an HTML table like this next answer box:

Yes Not yet Not sure

 

A-2. I know how to write an HTML document like this diagnostic exam:

Yes Not yet Not sure

 

A-3. I know how to write a script that processes an exam like this one:

Yes Not yet Not sure

 
This is based on a diagnostic quiz from Statistics by Freedman, Pisani, & Purves.