Sample Test I MATH 3032


For the first set of problems consider a data set with the following characteristics:

Median --- 95

Mean ---- 100

Mode ----- 92

Standard deviation - 15

First Quartile ----- 75

Third Quartile ---- 130

Minimum -- 50

Maximum - 190

1. Draw a box and whisker chart for the data. (4 points)

2. About what portion of the data are below 130? (4 points)

For the next set of problems consider a data set with a normal distribution and the following characteristics:

Median -- 100

Mean ---- 100

Mode ---- 100

Standard deviation - 15

First Quartile ----- 85

Third Quartile ---- 120

Minimum -- 65

Maximum - 190

3. What portion of the scores are above 130? (4 points)

4. What is the z-score for a score of 140? (4 points)

5. Draw a box and whisker chart for the data. (4 points)


6. Given the following set of data calculate the requested statistics.

{ 1, 21, 18, 20, 3, 31, 35, 30, 21 }

a. Mean (4 points)

b. Median (3 points)

c. Mode (2 points)

d. Third Quartile (2 points)

e. Variance (4 points)

f. Standard Deviation (2 points)

7. Draw a rectangular dart board on part of the below grid so that you can arrange regions so that the probability of each is as follows: (8 points)

A -- 1/6

B -- 1/8

C -- 5/16

D -- remainder

8. Draw a spinner so that the probability of Green is 1/2 while the probability of red is 1/3. (4 points)

9. The following probability tree is for the experiment pick two marbles, without replacement, from the bag with 5 Red and 2 White marbles. Use the tree disgram to answer the following questions.

a. P(R W) (3 points)

b. P(2 marbles of the same color) (5 points)

c. P(at least one red) (5 points)

10. The odds against Tallahassee winning the race are 11 to 3. What is the probability of Tallahassee winning? (4 points)

11. A bag contains the following marbles -- 7 Red, 2 White, and 1 Blue. Find the following.

a. P(Red)(3 points)

b. P(White)(3 points)

c. P(Blue) (3 points)

d. If you get a blue marble you win $100, for white you win $50, otherwise you lose $30. What is the expected valus of the game? (6 points)

12. There are eight parents willing to help with the soccer team. In how many ways can you pick 2 coaches and a scorekeeper? (5 points)

13. The heights of 500 girls at Southbrook High were measured, and the mean was found to be 160 cm with a standard deviation of 5 cm. If the heights are approximately normally distributed how many of the girls are:

a. over 170 cm tall? (5 points)

b. between 130 and 170 cm tall? (5 points)

14. Express the following as factorials. (3 points each)

a. Combinations of 10 taken 3 at a time.

b. Permutations of 7 taken 4 at a time.

c. Combinations of 52 taken 7 at a time.

15. The box and whisker plot below gices information concerning class scores on an English test. Use it to answer the questions which follow. (3 points each)

a. What is the range of scores?

b. What is the median score?

c. What is the upper quartile score?

d. What percent of the students ascored below 70?

e. What percent scored between 70 and 85?

16. If P(A) is 75% then the odds on A are? (3 points)

17. If the odds on A are 10 to 1 against then what is the probability of A?

18 Draw the probability tree for a best 2 out of 3 tournament where the probability that Chicago wins a given game is 2/3. (7 points)

19. Consider the polygon shown:

a. The sum of the measures of the interior angles is? (5 points)

b. The measures of the two missing angles are? (4 points)

20. Consider the following figure and calculate the measures of the requested angles. The two horizontal lines are parallel. (3 points each)

a. Angle 1

b. Angle 2

c. Angle 3

d. Angle 4

e. Angle 5

f. Angle 6

21. Given a triangle and a circle draw examples where they intersect at exactly the requested number of points. (3 points each)

a. Four

b. Five

22. The measure of angle 1 is 10 degrees more than twice that of angle 2. If the two angles are supplementary what is the measure of angle 1? (3 points)

23 How many sides are there in a regular polygon with a vertex angle of 176 degrees? (4 points)

24. What is the maximum number of points of intersection between a triangle and a hexagon if there are no line segments in the intersection? (4 points)

25. Given that vertex A of triangle A,B1,C1 coincides with that of A,B2,C2 while segment AB1 is a subset of AB2 and AC1 is a subset of AC2 with segment B1C1 parallel to B2C2 if AB1=2 while AB2=5 what is the length of B2C2 in terms of the length of B1C1? (4 points)

26. If you have a right pentagonal prism where the base is a regular pentagon describe all of the faces of the prism. (5 points)

27. If you have a right hexagonal pyramid where the base is a regular hexagon describe all of the faces of the pyramid. (5 points)

28. How many planes of symmetry are there in a right octagonal pyramid? (3 points)

29. Apply Euler's formula to a truncated right square pyramid and show how it works. (3 points)

30. Slicing a cube with a plane show how the intersection can be an equilateral triangle. (3 points)


This page updated by Frank Matthews Sept. 25, 2003