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Quantitative Math

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Submitted By nubiadeity
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MAT 143
Exam
Must Show Work 1. Decide whether the following statements make sense and why?

a. Restaurant prices have increased by 100% in the last 20 years

b. I have a 70% average on our assignments going into the final exam, but I still hope to raise my course average to 80% by getting an 95% on the final. (The final is worth 25% of the final grade.)

2. Fill in the blanks (Reduce Fractions): Percent | Decimal | Fraction | 130% | | | | .072 | | | | 5/8 |

3. Assume that 40% of voters registered voters in Raleigh are Republicans. Read the following questions carefully, and give the most appropriate answers. a. The percentage of voters registered, as Republicans is 25% higher in Boone than in Raleigh. What percentage of the registered voters in Boone are Republicans?

b. The percentage of voters registered as Republicans is 25 percentage points high in Boone than in Raleigh. What percentage of the registered voters in Boone are Republicans?

4. a. The number of housing foreclosures in 2008 was 3.98 million, up 78% over 2007. How many foreclosures were there in 2007?

b. Your dinner bill is $44.50. You leave $50. Ignoring taxes, what percent tip did you leave? 5. Joe pays a semiannual premium of $750 for automobile insurance, and monthly premium of $150 for health insurance, and an annual premium of $500 for life insurance. Prorate the following expenses and find the corresponding monthly expense.

6. Find the net monthly cash flow (it could be positive or negative). Assume that salaries and wages are after taxes, and assume 1 month = 4 weeks.

Income Expenses
Part-time job: $650/month Rent: $450/month
College fund from Groceries: $80/week grandparents: $400 month Tuition & fees: $3500
Scholarship: $5000/year twice a year Entertainment: $50/week Phone: $65/month

7. Two drugs, A & B, were tested on a total of 2000 patients, half of whom were women and half of whom were men. Drug A was given to 900 patients, and Drug B to 1100 patients. The results appear in the table below. | Women | Men | Drug A | 5 of 100 cured | 400 of 800 cured | Drug B | 101 of 900 cured | 196 of 200 cured | a. Give numerical evidence to support the claim that Drug B is more effective than Drug A.

b. Give numerical evidence to support the claim that Drug A is more effective than Drug B.

Which claim makes more sense? Why?

For questions 8- 10 use the formula
PMT=P X APRn1-1+APRn(-nY) 8. Suppose you have a credit card balance of $4500 with an annual interest rate of 22%. You decide to pay off your balance over 2 years. How much will you need to pay each month? Assume you make no further credit card purchases.

9. You need a $15,000 loan to buy a used car. You bank offers a 3-year loan at 3.5%, a 4-year loan at 4%, and a 5-year loan at 6%. Calculate your monthly payments and total interest over the loan term with each option.

10. Suppose you have a student loan of $32,000 with an APR of 6% for 20 years. a. What are the required monthly payments

b. Suppose you would like to pay the loan off in 15 years instead of 20. What monthly payments would you need to make?

c. Compare the total amount you’ll pay over the loan term if you pay the loan off in 10 years versus 15 years.

Use the formula A=PMT X 1+APRnnY-1APRn for questions 11-12

11. Find the savings plan balance after 10 years with an APR of 5% and a monthly payment of $400.

12. At age 25 you start saving for retirement. If your investment plan pays an APR of 6% and you want to have $500,000 when you retire in 40 years, how much should you deposit monthly?

13. The following table shows real arrival data for two airlines in five cities (airline names have been changed). Excelsior Airlines Paradise Airlines Destination | % On Time | # of Arrivals | % On Time | # of Arrivals | Los Angeles | 88.9 | 559 | 85.6 | 811 | Phoenix | 94.8 | 233 | 92.1 | 5255 | San Diego | 91.4 | 232 | 85.5 | 448 | San Francisco | 83.1 | 605 | 71.3 | 449 | Seattle | 85.8 | 2146 | 76.7 | 262 | | | | | | Total | | 3775 | | 7225 |

a. Which airline has the higher percentage of on-time flights to the five cities?

b. Compute the percentage of on-time flights for the two airlines over all five cities?
c. Explain the apparent inconsistency in these results

14. Suppose you are a scheduler for an airline, analyzing a distribution of flight delays (departures) during one day at an airport. The distribution of delay times has the following properties: The mean delay is 10 minutes, the median delay is 6 minutes, the mode of the distribution is 0 minutes, and the maximum delay is 25 minutes. a) Draw a rough sketch of the distribution with clearly labeled axes. Is the distribution right-skewed, left-skewed, or symmetric? b) What percentage of flights were delayed less than 6 minutes? c) What percentage of flights were delayed more than 6 minutes? d) Discuss the pros and cons of using the mean and the median to present the average flight delay of your airline to the public.

15. You toss three coins 1000 times; the following table shows the results. Compute the experimental probability for each event. Compare the experimental probabilities to the theoretical probabilities for three tossed coins. Do you have reason to believe the coins are unfair? Explain.

Result | # of Occurrences | 0 heads | 260 | 1 head | 495 | 2 heads | 245 | 3 heads | 0 | Total | 1000 |

17. The population of MeadowView is increasing at a rate of 300 people per year. If the population is 2500 today, what will it be in four years?

18. The price of high-definition TV sets has been falling by about 25% per year. If the price is $1000 today, what can you expect it to be in two years?

19. Consider the following statements about a correlation. In each case, state correlation clearly. Then state whether the correlation is most likely due to coincidence, a common underlying cause, or a direct cause. Explain your answer. a. In a large resort city, the crime rate increased as the number of taxi cabs increased.

b. When gasoline prices rise, sales of sport utility vehicles decline

20. The population of a town with an initial population of 60,000 grows at a rate of 2.5% per year. Create an exponential function to model the situation. Predict the population in 10 years.

21. Assume that for the average individual aspirin has a half-life of 8 hours in the bloodstream. At 12:00 noon, you take a 300-mig dose of aspirin. a. How much aspirin will be in your blood at 6:00 pm the same day?

b. Estimate when the amount of aspirin will decay to 5% of its original amount.

Find the percent change in Females with a Doctoral Degree vs Men with a Doctoral Degree

Within a group of 800 typical first-year students how many support a national health care plan?
10. The graphic on the previous page is a map of New Zealand and a bar graph demonstrating global air pollution.
a.) Which countries have safe levels of air pollution according to the World Health Organization’s standards?

b.) What country produces the most air pollution and how much does it produce?

c.) How many times more pollution do they produce than the USA? What about China?

d.) What part of the world are the largest polluters? Why might this be?

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