Lazurus Steel Corporation produces iron rods that are supposed to be 33 inches long. The machine that makes these rods does not produce each rod exactly 33 inches long. The lengths of the rods vary slightly. It is known that when the machine is working properly, the mean length of the rods made on this machine is 33 inches. The standard deviation of the lengths of all rods produced on this machine is always equal to 0.3 inch. The quality control department takes a sample of 23 such rods every week, calculates the mean length of these rods, and makes a 99% confidence interval for the population mean. If either the upper limit of this confidence interval is greater than 33.10 inches or the lower limit of this confidence interval is less than 32.9 inches, the machine is stopped and adjusted. A recent sample of 23 rods produced a mean length of 33.06 inches. Based on this sample, will you conclude that the machine needs an adjustment? Assume that the lengths of all such rods have a normal distribution. Round to two decimal places.

The confidence interval is...

Greta, an elderly investor, has a degree of risk aversion of A = 3 when applied to return on wealth over a one-year horizon. She is pondering two portfolios, the S&P 500 and a hedge fund, as well as a number of one-year strategies. (All rates are annual and continuously compounded.) The S&P 500 risk premium is estimated at 6.8% per year, with a SD of 21.8%. The hedge fund risk premium is estimated at 11.8% with a SD of 36.8%. The returns on both of these portfolios in any particular year are uncorrelated with its own returns in other years. They are also uncorrelated with the returns of the other portfolio in other years. The hedge fund claims the correlation coefficient between the annual returns on the S&P 500 and the hedge fund in the same year is zero, but Greta is not fully convinced by this claim.

Calculate Greta’s capital allocation using an annual correlation of 0.3. (Do not round your intermediate calculations. Round your answers to 2 decimal places.)

A particular college has a 30% graduation rate. If 212 students are randomly selected, answer the following.

a) Which is the correct wording for the random variable? Select an answer

b) Pick the correct symbol: ? = 212 c) Pick the correct symbol: ? = 0.3

d) What is the probability that exactly 65 of them graduate with a degree? Round final answer to 4 decimal places.

e) What is the probability that less than 65 of them graduate with a degree? Round final answer to 4 decimal places.

f) What is the probability that more than 65 of them graduate with a degree? Round final answer to 4 decimal places.

g) What is the probability that exactly 66 of them graduate with a degree? Round final answer to 4 decimal places.

h) What is the probability that at least 66 of them graduate with a degree? Round final answer to 4 decimal places.

i) What is the probability that at most 66 of them graduate with a degree Round final answer to 4 decimal places

1. An agronomist randomly sampled 18 certified organic apples and 42 “regular” (not certified organic) apples. (Multiple varieties were selected.) The organic apples had a mean weight of 3.4 ounces with a standard deviation of 0.4 ounces. The agronomist also confirmed that the weights of the organic apples were roughly normally distributed. The regular apples had a mean weight of 3.9 ounces with a standard deviation of 0.3 ounces. The agronomist will be testing the hypothesis that the mean weight of an organic apple is less than the mean weight of a “regular” apple.

1. Conduct an appropriate hypothesis test of the claim. [Be sure to state the hypotheses, find the test statistic, find the p-value or critical value (either is OK), and draw the appropriate conclusion about the claim.]
2. Why didn’t the agronomist bother to check that the weights of regular apples were roughly normal?
3. If the weights of the organic apples had turned out to be clearly bimodal with a couple of extreme outliers, which test should we have used instead?

Greta, an elderly investor, has a degree of risk aversion of A = 3 when applied to return on wealth over a one-year horizon. She is pondering two portfolios, the S&P 500 and a hedge fund, as well as a number of one-year strategies. (All rates are annual and continuously compounded.) The S&P 500 risk premium is estimated at 7.6% per year, with a SD of 22.6%. The hedge fund risk premium is estimated at 12.6% with a SD of 37.6%. The returns on both of these portfolios in any particular year are uncorrelated with its own returns in other years. They are also uncorrelated with the returns of the other portfolio in other years. The hedge fund claims the correlation coefficient between the annual returns on the S&P 500 and the hedge fund in the same year is zero, but Greta is not fully convinced by this claim.

Calculate Greta’s capital allocation using an annual correlation of 0.3. (Do not round your intermediate calculations. Round your answers to 2 decimal places.)

Greta, an elderly investor, has a degree of risk aversion of A = 3 when applied to return on wealth over a one-year horizon. She is pondering two portfolios, the S&P 500 and a hedge fund, as well as a number of one-year strategies. (All rates are annual and continuously compounded.) The S&P 500 risk premium is estimated at 7.6% per year, with an SD of 22.6%. The hedge fund risk premium is estimated at 12.6% with an SD of 37.6%. The returns on both of these portfolios in any particular year are uncorrelated with its own returns in other years. They are also uncorrelated with the returns of the other portfolio in other years. The hedge fund claims the correlation coefficient between the annual returns on the S&P 500 and the hedge fund in the same year is zero, but Greta is not fully convinced by this claim.

Calculate Greta’s capital allocation using an annual correlation of 0.3.

(Do not round your intermediate calculations. Round your answers to 2 decimal places.)

S&P_________%

Hedge___________%

Risk-Free Asset_________%

A site is underlain by

sand (0 to 3 meters; unit weights = 18 and 20 kN/m ³, K = 0.5, e ₀ = 0.55, and OCR = 1); followed by

clay (3 to 8 meters; unit weights = 20 and 22 kN/m ³, K = 0.6, c _r = 0.02, c _c = 0.3, c _v = 0.2 m ²/day, e ₀ = 0.8, and OCR = 2); followed by

gravel (8 to 10 meters; unit weights = 18 and 20 kN/m ³, K = 0.5, e ₀ = 0.62, and OCR = 1); followed by

rock. The unit weight of water is 10 kN/m ³. The water table is at the ground surface.

Utilize a point in the middle of the clay layer to determine the ultimate consolidation settlement of the clay layer if a 150 kPa fill is placed on the site. Express your answer in meters, but only write the numeric value in the text box.  Suggestion: draw the profile on paper.

Correct Answer is 0.2 m

Greta, an elderly investor, has a degree of risk aversion of A = 3 when applied to return on wealth over a one-year horizon. She is pondering two portfolios, the S&P 500 and a hedge fund, as well as a number of one-year strategies. (All rates are annual and continuously compounded.) The S&P 500 risk premium is estimated at 8.2% per year, with a SD of 23.2%. The hedge fund risk premium is estimated at 13.2% with a SD of 38.2%. The returns on both of these portfolios in any particular year are uncorrelated with its own returns in other years. They are also uncorrelated with the returns of the other portfolio in other years. The hedge fund claims the correlation coefficient between the annual returns on the S&P 500 and the hedge fund in the same year is zero, but Greta is not fully convinced by this claim.

Calculate Greta’s capital allocation using an annual correlation of 0.3. (Do not round your intermediate calculations. Round your answers to 2 decimal places.)

S&P=

Hedge=

risk-free asset=

Greta, an elderly investor, has a degree of risk aversion of A = 3 when applied to return on wealth over a one-year horizon. She is pondering two portfolios, the S&P 500 and a hedge fund, as well as a number of one-year strategies. (All rates are annual and continuously compounded.) The S&P 500 risk premium is estimated at 8.4% per year, with a SD of 23.4%. The hedge fund risk premium is estimated at 13.4% with a SD of 38.4%. The returns on both of these portfolios in any particular year are uncorrelated with its own returns in other years. They are also uncorrelated with the returns of the other portfolio in other years. The hedge fund claims the correlation coefficient between the annual returns on the S&P 500 and the hedge fund in the same year is zero, but Greta is not fully convinced by this claim.

Calculate Greta’s capital allocation using an annual correlation of 0.3. (Do not round your intermediate calculations. Round your answers to 2 decimal places.)

The Neal Company wants to estimate next year's return on equity (ROE) under different financial leverage ratios. Neal's total capital is $14 million, it currently uses only common equity, it has no future plans to use preferred stock in its capital structure, and its federal-plus-state tax rate is 40%. The CFO has estimated next year's EBIT for three possible states of the world: $4.9 million with a 0.2 probability, $2.5 million with a 0.5 probability, and $0.7 million with a 0.3 probability. Calculate Neal's expected ROE, standard deviation, and coefficient of variation for each of the following debt-to-capital ratios. Do not round intermediate calculations. Round your answers to two decimal places at the end of the calculations.

1) Debt/Capital ratio is 0.

2)Debt/Capital ratio is 10%, interest rate is 9%.

3) Debt/Capital ratio is 50%, interest rate is 11%.

4) Debt/Capital ratio is 60%, interest rate is 14%.