# statistics test answers: What is the range?

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Question 2

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

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?

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?

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?

(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

1. Which class had a higher percentage of students scoring an A (90 or better)?
2. 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.

1. 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?
2. 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?
1. 5 * \$8.20 = \$41 per week * 52 = \$2132
1. 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.

1. How much money, in total, will you have in the mutual fund if you choose Option A?
2. How much money, in total, will you have in the mutual fund if you choose Option B?
3. 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.

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 daysFor each of the following questions, round to the nearest cent and include units with your final answers.

1. What is the balance at the end of November?
2. What is the finance charge for November?
1. Finance charge 1375 * 24%/12 = 27.5 + 1375 + 175.16 – 380 + 65.97 = 1263.63
2. 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.

1. How much total interest will you have paid at the end of the three years?
2. What is the yearly interest rate?
1. 91.09 * 36 – 1699 = 3279.24 – 1699 = 1580.24
2. 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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