24SP MATH 101 Mathematics for Liberal Arts

Homework Week

1. What percent of the standard normalz-distribution lies between the following values? (Round all answers to two decimal places.)

(a)z= 0 andz=2 _________% (b)z=-2andz= 0 _________% (c)z=-2andz=2(Note: This interval representstwostandard deviations of the mean.) __________%

2.What percent of the standard normalz-distribution lies betweenz=-1.5andz= 0? (Round your answer to two decimal places.) ________________%

3.Find the following probabilities. (Round all answers to four decimal places.)

(a)p( 0 <z<1.68)

_____________ (b)p(1.20<z<1.87) _____________ (c)p(z<-1.87) _____________

4. Findcsuch that each of the following is true. (Round all answers to two decimal places.)

(a)p( 0 <z<c) =0.1736 ___________ (b)p( -c<z<c) =0.4648 ___________ (c)p(z>c) =0.6368 ___________

5. A population is normally distributed with mean36.8and standard deviation2.5. Find the following probability. (Round your answer to four decimal places.)

p(36.8<x<39.3)

___________

6. Use the body table to find the specifiedz-number. (Round the answer to two decimal places.)

(a)z_0.4279=________ (b)z_0.3997=________ (c)z_0.3790=________ (d)z_0.4951=________

7.Find thez-number associated with a80%level of confidence. (Round the answer to two decimal places.) z= __________

8. A survey asked, "How important is it to you to buy products that are made in America?" of the 600 Americans surveyed, 450 responded, "It is important." For each of the following levels of confidence, find the sample proportion and the margin of error (MOE) associated with the poll. (Give the answers to one decimal place, if needed.)

(a) A 90% level of confidence Sample proportion is __________% MOE =________% (b) A 95% level of confidence Sample proportion is_________% MOE =____________%

9. A survey asked, "Do you think that homeless people are responsible for the situation they are in?" Of the2,500Americans surveyed,1,408said no.

(a) Determine the sample proportion of Americans who think that homeless people are not responsible for the situation they are in. (Round your answer to the nearest whole number.) Sample proportion is__________% (b) With an80%level of confidence, find the margin of error (MOE) associated with the sample proportion. (Give the answer to one decimal place, if needed.) MOE =__________% (c) With a95%level of confidence, find the margin of error (MOE) associated with the sample proportion. (Give the answer to one decimal place, if needed.) MOE =__________% (d) The answer in part (c) issmaller thanOR larger thanthe answer in part (b). Why? In order to guarantee 95% accuracy, we mustdecrease OR increasethe error.

10.Find the simple interest of$4,000borrowed at7%for3years. (Round your answer to the nearest cent.) I= $ ____________

11. Find the future value of$3,670borrowed at3 1/4%simple interest for9years. (Round your answer to the nearest cent.) FV= $ ____________

12. Find the maturity value of$1,300borrowed at6 5/8%simple interest for7years. (Round your answer to the nearest cent.) FV= $__________

13. Find the present value of the future value of$9,200at7 1/2%simple interest for5years. (Round your answer to the nearest cent.) P= $ ___________

14. Tina and Mike have sold their house, but they will not get the proceeds from the sale for an estimated3months. The owner of the house they want to buy will not hold the house that long. Tina and Mike have two choices: let their dream house go or take out a bridge loan. The bridge loan would be for$85,000, at7.5%simple interest, due in90days. How much interest would they pay for this loan? (Round your answer to the nearest cent.) $___________

15. Find the future value of$3,000at5%compounded annually for12years. Ignore leap years. (Give your answers to the nearest cent.) FV= $ _______

16. Find the annual yield corresponding to the nominal rate of6%compoundeddaily. (Round the answer to two decimal places.) r= _________%

17. Find the present value that will generate the future value of$1,000at7%compounded yearly for6years. (Give your answer to the nearest cent.) P= $ ____________

18. A certificate of deposit (CD) is an agreement between a bank and a saver in which the bank guarantees an interest rate and the saver commits to leaving his or her deposit in the account for an agreed-upon period of time. National Trust Savings offers 5-year CDs at 8.25% compounded daily, and Bank of the Future offers 5-year CDs at 8.28% compounded annually. Compute the annual yield for each institution, and determine which is more advantageous for the consumer. (Round your answers to two decimal places.)

NTS:	r=___________%
BF:	r=___________%

Bank of the Future OR National Trust Savingshas the better offer.

19. A certificate of deposit (CD) is an agreement between a bank and a saver in which the bank guarantees an interest rate and the saver commits to leaving his or her deposit in the account for an agreed-upon period of time. National Trust Savings offers 5-year CDs at 8.25% compounded daily, and Bank of the Future offers 5-year CDs at 8.28% compounded annually. Compute the annual yield for each institution, and determine which is more advantageous for the consumer. (Round your answers to two decimal places.)

NTS:	r=_______%
BF:	r=_______%

Bank of the Future OR National Trust Savingshas the better offer

20.When Jason Levy was born, his grandparents deposited $3,000 into a special account for Jason's college education. The account earned 6 1/2% interest compounded daily. How much will be in the account when Jason is 18? (Give your answer to the nearest cent.) FV= $ ________

21.Find the following probabilities. (Round all answers to four decimal places.)

(a)p(-0.87<z<1.65) ___________ (b)p(-2.31<z<-1.18) __________ (c)p(z<1.52) _________

22. When asked, "Do kids regularly carry weapons in your school?"14,255students said yes, and115,335students said no. With a95%level of confidence, find the margin of error (MOE) associated with the sample proportions. (Give the answer to one decimal place, if needed.) MOE = __________%

23.Find the number of periods that corresponds to the time span of50years for each period shown below. (Ignore leap years.)

(a) a quarter of a year ______ (b) a month_______ (c) a day________