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 ----- 85

Third Quartile ---- 110

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 110? (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 value 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 gives 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? (3 points)

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. Suppose that you flip 6 coins and count the number of heads. (3 points each)

(a) What is the probability of at least four heads?

(b) How many ways can 3 heads occur?

20. How many triangles are there in the figure? (6 points)

21. When rolling a pair of green & red dice what is the conditional probability of getting a sum over eight given that the green die has more than four spots? (5 points)

22. How many feet in a mile? (3 points)

23 How many cups in a quart? (3 points)

24 How many yards in a furlong? (3 points)

25. The mean average score of an English test taken by 28 students is 73. If 2 more students take the test and the combined score is then 72, what is the average score of the two students? (6 points)

26. What percentile represents a z-score of -2? (4 points)

27. An experiment is to roll a die, pick a letter from the English alphabet, and then flip a coin. How many different ways can this happen? (3 points)

27. A game consists of rolling a pair of dice. If a double 1 pays $7.50, a double 5 $3.00, and a sum of 5 pays $1.00, while everything else pays nothing what is the expectation? (5 points)

28. What are the two numbers before and after the following?

_____, _____, 400_twelve ______, ______ (4 points)

29. Convert 4 2 6 _nine to base ten. (5 points)

30. Convert 5 2 6 from base ten to base twelve. (5 points)

31. Compute the following addition problem in base twelve. 4 6 8 + 5 7 9_twelve

(4 points)

32. Compute the following multiplication problem by the lattice method in base five.

324 x 42_five

(5 points)

This page updated by Frank Matthews Feb. 23, 2009