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**Question 2**

The following values are the number of hours spent working each week for ten randomly selected students:

20 | 0 | 35 | 20 | 20 | 13 | 15 | 20 | 0 | 35 |

What is the range?

What is the mean?

**Question 4**

The SAT is an exam used by colleges and universities to evaluate applicants. The SAT scores are normally distributed with a mean of 1425 and a standard deviation of 326. What percent of students scored above 2077 on the SAT?

a. | 2.5% | |

b. | 16% | |

c. | 2.35% | |

d. | 97.5% |

100 -95 = 5% / 2 = 2.5%

**Question 5**

The SAT is an exam used by colleges and universities to evaluate applicants. The SAT scores are normally distributed with a mean of 1498 and a standard deviation of 316. What percent of students scored between 866 and 1814 on the SAT?

a. | 95% | |

b. | 81.5% | |

c. | 83.85% | |

d. | 47.5% |

1498 to 866 = 95%/2 = 47.5%

1498 to 1814 = 68%/2 = 34%

47.5% + 34% =81.5%

**Question 6**

The SAT is an exam used by colleges and universities to evaluate applicants. The SAT scores are normally distributed with a mean of 1498 and a standard deviation of 316. Of 2500 randomly selected students who took the SAT, how many of them scored below 1182?

a. | 16 | |

b. | 63 | |

c. | 400 | |

d. | 1,250 |

(100% – 68%) / 2 = 32% /2 = 16%

16% * 2500 = 400

**Question 7**

Suppose you earn an 87 on your biology test that had a mean score of 78 with a standard deviation of 4. You also earned an 88 on a math test that had a mean score of 80 with a standard deviation of 5. The exam scores in both classes follow a normal distribution. Which exam had more consistent grades? *Justify your answer mathematically for full credit.*

The math test had more consistent grades since the score is closer to the class mean. The z score for math test is 1.6 which is more stable than the biology test which was 2.25

**Question 8**

Suppose you earn an 87 on your biology test that had a mean score of 78 with a standard deviation of 4. You also earned an 88 on a math test that had a mean score of 80 with a standard deviation of 5. The exam scores in both classes follow a normal distribution

- Which class had a higher percentage of students scoring an A (90 or better)?
- What is the corresponding percentage?

100%-95% = 5%/2 = 2.5%

**Question 9**

Billy buys seven lottery tickets each week at a cost $2 each and spends $200 per month on food. On an **annual** basis, the first set of expenses is ________% of the second set of expenses

7*$2= $14 PER WEEK

Per year $14 * 52 weeks = $728 on lottery tickets per year

$200 *12 = $2400 on food per year

$728/$2400 *100% =30.33%

**Question 10**

Emily plans to create a budget to more effectively manage her money. To help understand where her money is going, she lists several of her expenses. *Assume there are 4 weeks in a month and 52 weeks in a year and include appropriate units with your final answer.*

- Emily gets lunch from a fast-food restaurant each weekday (Monday – Friday). After tax, her lunch costs $8.20 per day. How much does she spend annually on lunch?
- Emily decides to start bringing her lunch from home each weekday instead of buying lunch. To make her lunch at home it costs $2.10 each weekday. How much money will she
**save**annually by bringing her lunch from home?

- 5 * $8.20 = $41 per week * 52 = $2132
- 5 * (8.20 -2.10) = $30.5 saved per week * 52 = $1586

**Question 11**

You have a simple interest account that you invested $600 into 4 years ago. Currently there is $816 in the account and no deposits or withdrawals have been made. What is the annual simple interest rate of this account? *Express your answer as a percentage and round your final answer to two decimal places if needed.*

*I=prt*

*816-600 = 600 * r * 4*

*216= 2400r*

*R = 216/2400 * 100%*

*R = 9%*

**Question 12**

You have the opportunity to invest $14,000 with an annual interest rate of 9% in a mutual fund. There are two mutual funds you can choose from. Option A: is a 9 year fund that compounds monthly. Option B: is an 8 year fund that compounds quarterly. *For each of the following questions, round to the nearest cent and include units with your final answers*.

- How much money, in total, will you have in the mutual fund if you choose Option A?
- How much money, in total, will you have in the mutual fund if you choose Option B?
- Which is the better option for you to choose?

**Question 13**

Students at Wake Tech pay $1,200 in tuition each semester (spring and fall) to attend. Students also pay $500 for books each semester. Summer school costs $1,020 with books costing $185. Prorate the given expenses to find the **monthly** cost. *Round the final answer to two decimals places as needed.*

*Tuition = 1200* 2 = 2400*

*Books = 500*2 =1000*

*Summer school = 1020+ 185 = 1205*

*Total = 4605 per year*

*Monthly 4605/12 = 383.75*

**Question 14**

The table below lists a person’s income and expenses.Calculate the monthly net cash flow.

*Assume there are 4 weeks in one month.*

Income | Expenses | ||

Paycheck (per month) | $2,100 | Rent (per month) | $850 |

Babysitting (per week) | $150 | Groceries (per week) | $110 |

Student Loans (per month) | $240 | ||

Entertainment (per month) | $200 | ||

Phone (per month) | $90 | ||

Electricity/water/gas (per month) | $70 | ||

Car Payment (per month) | $350 | ||

Life Insurance (per year) | $520 |

Paycheck + babysitting per month = 2100 + (150*4) = $2700

Expenses = 850 + 4(110) + 240 + 200 + 90 + 70 + 350 + (520/12) = 2283.33

Net = 2700 – 2283.33 = 416.67

**Question 15**

Gloria has a credit card with a 24% annual interest rate. Her balance at the end of October was $1,375. In November, she made the following transactions.

- November 8th: A purchase of $175.16 worth of groceries
- November 20th: A payment to the credit card company of $380
- November 28th: A purchase of $65.97 for dinner

The card calculates interest using the un-paid balance method. (*November has 30 days*) *For each of the following questions, round to the nearest cent and include units with your final answers*.

- What is the balance at the end of November?
- What is the finance charge for November?

- Finance charge 1375 * 24%/12 = 27.5 + 1375 + 175.16 – 380 + 65.97 = 1263.63
- 1263 * 2% per month

**Question 16**

You purchase a new laptop from an electronics store and use their in-store financing to pay for it. The laptop price is $1,699, but you will “only” pay $91.09 per month for three years. Later, you read the fine print and find out that your monthly payments are calculated using the add-on method. *Round all final answers to the nearest hundredths and include appropriate units.*

- How much total interest will you have paid at the end of the three years?
- What is the yearly interest rate?

**91.09 * 36 – 1699 = 3279.24 – 1699 = 1580.24**- 1580.24? 3 = 526.75 / 1699 * 100 % = 31%

**Question 17**

Find the future value of an ordinary annuity if the payment R = $300 is deposited monthly, the interest is compounded monthly at an annual rate of r = 5.5%, and the time is t = 15 years. *Include appropriate units and round all final answers to the nearest hundredths place.*

FVOrdinary Annuity=C×[*i*(1+*i*)*n*−1]

300 *{ [( 1+ 5.5/12) ^ 180 ] – 1 } / 5.5/12 300 * 4.5989 = 1379.

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