Math 101 for Liberal Arts

4/21/2024

Please complete the following questions with a detailed answer.

1. 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)_______

2. 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=

3. 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 = _________%

4. Find the maturity value of $1,300 borrowed at 6 5/8% simple interest for 7 years. (Round your answer to the nearest cent.) FV = $ __________

5. Tina and Mike have sold their house, but they will not get the proceeds from the sale for an estimated 3 months. 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, at 7.5% simple interest, due in 90 days. How much interest would they pay for this loan? (Round your answer to the nearest cent.) $ ____________.

6. Find the future value of $3,000 at 5% compounded annually for 12 years. Ignore leap years. (Give your answers to the nearest cent.) FV = $ ______

7. Find the annual yield corresponding to the nominal rate of 6% compounded daily. (Round the answer to two decimal places.) r = _______

8. Find the present value that will generate the future value of $1,000 at 7% compounded yearly for 6 years. (Give your answer to the nearest cent.) P = $ _________

9. 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. First National Bank offers 2-year CDs at 9.12% compounded daily, and Citywide Savings offers 2-year CDs at 9.13% compounded quarterly. Compute the annual yield for each institution and determine which is more advantageous for the consumer. (Round your answers to two decimal places.)

FNB:	r= %
CS:	r= %

10. 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= %

11. 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 = $ _________

12. 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)

________________

13. 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 = __________%

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

(a)z_0.4236= _________ (b)z_0.3997= __________ (c)z_0.3790= __________ (d)z_0.4946= ___________

15. A survey asked, "How important is it to you to buy products that are made in America?" of the 600 Americans surveyed, 150 responded, "It is not 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) An 85% level of confidence Sample proportion is _________ % MOE = ________ % (b) A 98% level of confidence Sample proportion is ___________ % MOE = __________%

16. The activity on Denise Hellings' Sears account for one billing period is shown below. Find the average daily balance and the finance charge if the billing period is March 1 through March 31, the previous balance was $157.14, and the annual simple interest rate is 21%. (Round your answer to the nearest cent.)

March 5	payment	$25.00
March 17	tools	$36.12

Average daily balance $ _________ Finance charge $ _________