The time until failure of the hard drives on laptops currently sold in the United States follows an exponential distribution, with a mean of 4.2 years. A company offers a special incentive program that guarantees a $500 refund if the hard drive on their laptops fails in the first year after purchase, and a $100 refund if the hard drive fails in the second year after purchase. Find the expected refund a customer would receive after purchasing one of this company’s laptops.

A study was conducted to determine if the salaries of librarians from two neighboring states were equal. A sample of 100 librarians from each state was randomly selected. The mean from the first state was $29,100 with a standard deviation of $2,200. The mean from the second state was $31,900 with a standard deviation of $2,150. Test the hypothesis that there is no difference in the salaries from both states at the 0.1 significance level.

determine the test statistic. Round to four decimal places.
t= ?????

An X-bar chart with three-sigma limits has parameters as follows:

• UCL = 104

• Center line = 100

• LCL = 96

• n = 9

Suppose that mean of the process quality characteristic shifts to 102, assume standard deviation does not change.

(a) What is average run length until the first point is plotted out of control?

(b) What is the probability that the control chart would exhibit lack of control by at least the third point plotted?

9) Suppose that t years from now, one investment will be generating profit at the rate of P 1 ′ = 40 + t 2 hundred dollars per year, while a second investment will be generating profit at the rate of P 2 ′ ( t ) = 100 + 4 t hundred dollars per year. For how many years does the rate of profitability of the second investment exceed that of the first? Compute the total net excess profit for the time period.

Tom borrows $100 at annual effective interest rate of 4% and agrees to repay it with 30 annual installments. The amount of each payment in the last 20years is set at twice that in the first 10 years. At the end of 10 years, Tom has the option to repay the entire loan with a final payment $X, in addition to the regular payment. This will yield the lender an annual effective rate of 4.5% over the 10-year period. Calculate $X? (ANS: 108.88)

1. You are considering a project that costs $500 to invest in today, and will pay you $100 next year. The cash inflow will grow at a constant rate of 3% per year after year 1, and you will receive cash inflows for 20 years (total including the first year CF). Your discount rate is 16%. What is the NPV of the project? Also, what would the NPV be if the cash inflows continued forever? Show your work.

The Sanding Department of Quik Furniture Company has the following production and manufacturing cost data for March 2017, the first month of operation. Production: 7,060 units finished and transferred out; 3,000 units started that are 100% complete as to materials and 20% complete as to conversion costs. Manufacturing costs: Materials $39,133; labor $21,100; overhead $40,103. Prepare a production cost report. (Round unit costs to 2 decimal places, e.g. 2.25.)

At a point in a bracket, the stress on two mutually perpendicular planes are 100 N/mm² (tensile) and 50 N/mm² (tensile). The shear stress across the planes is 80 N/mm². Find using Mohr stress circle or otherwise calculate:

1. Magnitude and direction of the resultant stress on plane making an angle of 20⁰ with the plane of the first stress.
2. Maximum shear stress and location of its plane.

c. Principal stresses and the location of principal planes