Finite Math : Statistics, Interest and the Time Value of Money

1. (5 pts) Which of the following can never be a negative number?

A. Sample variance
B. Sample mean
C. Maximum data value of a sample
D. Median of a sample

2. (5 pts) Which of the following statements is true?

A. Sample standard deviation is the central data value.
B. The variance is the square root of the standard deviation.
C. If all of the data values in a sample are identical, then the sample variance is 0.
D. To calculate the sample variance, add up the sum of the squares of the deviations from
The mean and then divide by n, the sample size.

3. (5 pts) How much money would have to be deposited now at 12% compounded annually, in order
to reach a balance of $3,000 in three years?

A. $2114.88
B. $2135.34
C. $2518.86
D. $4255.56

4. (5 pts) Which of the following graphs of a standard normal Z curve shows the shaded region
Corresponding to the probability Pr(-1.25 Z 2.0)?

GRAPH A

GRAPH B

GRAPH C

GRAPH D

End of MULTIPLE CHOICE

PART B. SHORT ANSWER (SHOW ALL WORK).

5. (16 pts) $6,000 is deposited into an account paying 8% interest compounded quarterly.

(a) State the interest rate per quarter.

(b) Complete the table showing the growth of the account for the first 3 quarters.
(Note: Some values will be repeated in the table. For example, the balance at the beginning of the second quarter is the same as the balance at the end of the first quarter.)

Report values to the nearest cent.

Quarter Balance at
Beginning of Quarter Interest Earned Balance at
End of Quarter
1
$6,000.00
$
$

2
$
$
$

3
$
$
$

(c) After 10 years (i.e., 40 quarters), what will be the balance? Use the compound amount formula to find the value. Show the formula with the appropriate values substituted and state the numerical result of the calculation, rounded to the nearest cent.

6. (20 pts) Compute the sample mean, the sample variance, and the sample standard deviation for the following set of data.
57 54 71 68 46 54 63

Use the table below to help organize your work. The last line of the table are the totals of the columns.

xi

57
54
71
68
46
54
63

_____

_____

______

Sample Mean = ________

Sample Variance = ________

Sample Standard Deviation = ___________

For QUESTION 8 Please give a brief summary on how you got your answer.

7. (5 pts) (Personal Finance Decisions) Give the ADD-ON Interest Rate. (EXPLAIN HOW YOU GOT YOUR ANSWER and SHOW ALL WORK)

A $10,000 loan for 2 years at 7% APR with a monthly payment of $447.73

8. (5 pts) Personal Finance Decisions Use the ADD-ON method to determine the monthly payment. (EXPLAIN HOW YOU GOT YOUR ANSWER and SHOW ALL WORK)

$3000 loan at 9% interest for three years
$6000 loan at 7% interest for one year
$10,000 loan at 8% interest for two years
9. (12 pts) For a certain game of chance, a player loses $3 with a probability of 0.3, breaks even with probability 0.3, gains $1 with probability 0.2, gains $2 with probability 0.1, and gains $3 with probability 0.1. This information is summarized in the table (extra space provided for computations.)

k Pr(X = k)

-3
0.3

0
0.3

1
0.2

2
0.1

3
0.1

(a) A player plays the game of chance. What is the probability that a player will win some money?

(b) If the player plays the game many times, what is the player's expectation?

(c)That is, what is the expected value (mean) of the probability distribution? Show work. (You are welcome to use the extra column and/or row in the table to make it easier to show the computation.)

10. (2 pts) Calculate the present value of a decreasing annuity of $1000 per year for 10 years at 6% interest compounded annually. (Show All Work)

11. (2 pts) Is it more profitable to receive $7000 now or $10,000 in 9 years. Assume that money can earn 4% interest compounded quarterly. (Show All Work)

12. (2 pts) (Light Bulb Lifetimes) Suppose that the lifetimes of a certain light bulb are normally distributed with u= 30,000 gallons and o = 4000. If the station has 39,000 gallons on hand at the beginning of the week, what is the PROBABILITY of its running out of gas BEFORE the end of the week? (Show All Work).

13. (22 pts) Suppose that shoppers at the Mini-Mart shop are studied, and the amount purchased by each shopper is recorded. It is determined that the purchase amounts are normally distributed, with a mean purchase of $9.00 and standard deviation of $2.50.

(a) What purchase amount is exactly one standard deviation above the mean?

(b) What purchase amount is exactly one standard deviation below the mean?

(c) Mary Smith's purchase was $4.00. What is her z-score? That is, calculate . Show some work.

(d) (Fill in the blanks) Mary Smith's purchase of $4.00 is _________ standard deviations
_________(choose above or below) the mean.

#13 (continued) Show work for all of the parts BELOW and EXPLAIN how you got your answer in simple terms.

(e) Find the probability that a randomly selected customer spends less than $4.00.

(f) Find the probability that a randomly selected customer spends between $4.00 and $14.00.

(g) Find the probability that a randomly selected customer spends more than $10.00.

(h) Find the 90th percentile of the purchases.