Let x be a random variable that represents the weights in kilograms (kg) of healthy adult female deer (does) in December in a national park. Then x has a distribution that is approximately normal with mean μ = 52.0 kg and standard deviation σ = 9.0 kg. Suppose a doe that weighs less than 43 kg is considered undernourished.
(a) What is the probability that a single doe captured (weighed and released) at random in December is undernourished? (Round your answer to four decimal places.)

(b) If the park has about 2850 does, what number do you expect to be undernourished in December? (Round your answer to the nearest whole number.)

(c) To estimate the health of the December doe population, park rangers use the rule that the average weight of n = 80 does should be more than 49 kg. If the average weight is less than 49 kg, it is thought that the entire population of does might be undernourished. What is the probability that the average weight x for a random sample of 80 does is less than 49 kg (assuming a healthy population)? (Round your answer to four decimal places.)

(d) Compute the probability that

x < 53.1 kg for 80 does (assume a healthy population). (Round your answer to four decimal places.)

Suppose park rangers captured, weighed, and released 80 does in December, and the average weight was

x= 53.1 kg. Do you think the doe population is undernourished or not? Explain.

Consider the following regression model. Weekend is whether or not the visit was on a weekend. Distance is how far the guests have to travel to get to the amusement park. Rides and Games are the number of rides and games, respectively. Clean is a cleanliness score from 1-10. Num.Child is the number of children with the guest. Wait is the average wait time for the rides.

Multiple R-squared: 0.8632,

Adjusted R-squared: 0.8787

F-statistic: 151.6 on 7 and 492 DF, p-value: .00000000022

Coeffiients:

Estimate Std. Error t value Pr(>ItI)

(Intercept) -140.61254 7.15405 -19.655 0.0000016

wekend -0.71573 0.80870 -0.885 0.376572

distance 0.04494 0.01219 3.686 0.000253

rides 0.61361 0.01219 5.072 0.0000059

games 0.13833 0.05872 2.356 0.18882

clean 0.92725 0.13593 6.821 0.000061

num.child 3.61602 0.26980 13.403 0.000025

wait 0.56476 0.04064 13.896 0.000031

a) do you think that this is a good regression model? Why or why not?

b)should all of the input variables in the model be included? If not, which variables should be removed from the model and why?

c) Generate a point estimate for the satisfaction level of an amusement park visit that is on a Friday, to an amusement park that is 63 miles away, that has 20 rides and 15 games. The park has a cleanliness score of 8, and an average wait time for each ride of 10 minutes. The guest has 3 children with them.

Personnel in a luxury hotel readily offer advice and recommendations about services and area activities. Complete each sentence with the correct verb form, either the infinitive, present indicative, or present subjunctive, according to the context.

Problem 2. The US National Park Service (NPS) believes that airborne sulfur pollution and acid rain has significantly reducing the water quality in several lakes and streams in the Adirondacks State Park in NY. Many of these water bodies are considered biologically ‘dead.’ Coal fired power plants in the Midwest contribute most of the pollution. If 70% of the sulfur pollution was removed, the NPS believes that many of the lakes and streams would return to their natural biological state. The costs and benefits associated with this project are as follows:

1. Construction cost for sulfur removal equipment = $300 million for each of the first three years of the project. (During these three years there are no other costs associated with the project.)

2. Operation and maintenance costs = $ 85 million per year (These costs begin to accrue once the project comes on-line in the fourth year. They continue to accrue over the entire life of the equipment, i.e., through the 20th year.)

3. Estimated increase in revenues earned by the Adirondacks State Park = $ 150 million per year (These additional revenues accrue so long as the sulfur reduction equipment is operating.)

4. Reduced incidence of acid rain in the Adirondacks Park area valued at: = $ 2 million per year. (These benefits begin accruing once the project comes on-line and are assumed to continue over an infinitely long time period.) Assume that the discount rate is 3% per year.

Sensitivity analysis: To determine the sensitivity of your conclusion regarding whether the project makes economic sense or not, (a) evaluate the project at a discount rate of 5% per year, and (b) assume that the estimated increase in Park revenues is $130 million per year instead of $150 million per year. You can assume a discount rate of 3% per year for this. What is your conclusion now?

Policy recommendation: Based on all your calculations, what is your overall recommendation regarding this project?

PROBLEM IV Binghamton University is building a recreation center. The estimated construction cost is $12 million with annual staffing and maintenance costs of $750,000 over the 20-year life of the project (ie, t = 0, 1, 2, …, 19). At the end of the life of the project (ie, at t = 19), Binghamton expects to be able to sell the land for $4 million, though the amount could be as low as $2 million and as high as $5 million. Analysts estimate the first-year benefits (accruing at the end of the year of the first year, ie at t =1) to be $1.2 million. They expect the annual benefit to grow in real terms due to increases in population and income. Their prediction is an annual growth rate of 4 percent, but it could be as low as 1 percent or as high as 6 percent. Analysts also estimate the real discount rate for Binghamton to be 6 percent per year, though it could be a percentage point lower or higher.

1. Calculate the present value of net benefits for this project using the analysts’ predictions.

2. Investigate the sensitivity of the present value of net benefits to alternative projections within the ranges given by the analysts. Change only one assumption at a time, and try all possible combinations of assumptions (there are 27 possible combinations).

3. Based on your analysis on parts 1 and 2 of this problem, do you think Binghamton University should build the recreation center?

(13)Acme Logistics provides “less than truck load” (LTL) services throughout the U.S. They have several hubs where they use cross-docking to move goods from one trailer to another. Acme built its last hub 10 years ago, and it had 36 dock doors. The cost index at that time was 140, and the total cost was $6 million. Acme plans a new hub that will have 48 dock doors. The cost index now is 195, and Acme will use a capacity factor of 0.82. What is the estimated cost of the new hub?

(a) 8580534 (b) 9580534 (c) 10580534 (d) 11580534

Your employer is considering a capital project that involves installing a new manufacturing facility(to manufacture a new product) at a cost of $30,800,000. The facility will be built on land that was purchased in 2018 for $1,250,000. If the facility is not built on this land, the land will remain unused. The new manufacturing facility, if built, will be depreciated on a straight-line basis over five years, to a salvage value of $2,000,000. If the facility is built, the production there will cause an immediate increase in Inventory of $1,300,000. It will also cause immediate increases in Accounts Receivable of $5,900,000, Accounts Payable of $850,000, and Long-Term Debt of $15.2million.

If built and produced, the new product is expected to generate annual sales of $20,375,000 by the end of the first year. Sales are expected to increase 8% per year. COGS expense is expected to be of $9,780,000 during the first year. Thereafter, COGS is expected to remain at a constant percentage of Sales. Because operating efficiency is expected to improve each year, SG&A expense is expected to remain at $3,750,000 for each of the five years of the project. At the end of the project’s five-year life, production will cease, and the manufacturing facility will be sold for an estimated $4,500,000. At that time, Inventory, Accounts Receivable and Accounts Payable will return to their pre-project levels.

If the project is implemented, it will likely increase sales of the company’s existing complimentary products. The net impact of those sales is expected to be a $2,225,000 annual increase in pre-tax profits.

Your employer’s tax rate is 21%. The firm has 5 million shares of common stock outstanding. The firm requires a 11% rate of return on capital projects of this risk.

Prepare a discounted cash flow analysis to determine whether your employer should implement this capital project. Your analysis should reveal answers to each of the following questions. Clearly label all cells. Highlight the cells that answer the following questions:

1. What is the initial investment amount (Year 0)?
2. What are the total cash flows each year (Years 1-5)
3. What is the NPV?
4. What is the IRR?

Discounted Cash Flow Analysis (Model) Excel Case:

Your employer is considering a capital project that involves installing a new manufacturing facility(to manufacture a new product) at a cost of $30,800,000. The facility will be built on land that was purchased in 2018 for $1,250,000. If the facility is not built on this land, the land will remain unused. The new manufacturing facility, if built, will be depreciated on a straight-line basis over five years, to a salvage value of $2,000,000. If the facility is built, the production there will cause an immediate increase in Inventory of $1,300,000. It will also cause immediate increases in Accounts Receivable of $5,900,000, Accounts Payable of $850,000, and Long-Term Debt of $15.2million.

If built and produced, the new product is expected to generate annual sales of $20,375,000 by the end of the first year. Sales are expected to increase 8% per year. COGS expense is expected to be of $9,780,000 during the first year. Thereafter, COGS is expected to remain at a constant percentage of Sales. Because operating efficiency is expected to improve each year, SG&A expense is expected to remain at $3,750,000 for each of the five years of the project. At the end of the project’s five-year life, production will cease, and the manufacturing facility will be sold for an estimated $4,500,000. At that time, Inventory, Accounts Receivable and Accounts Payable will return to their pre-project levels.

If the project is implemented, it will likely increase sales of the company’s existing complimentary products. The net impact of those sales is expected to be a $2,225,000 annual increase in pre-tax profits.

Your employer’s tax rate is 21%. The firm has 5 million shares of common stock outstanding. The firm requires a 11% rate of return on capital projects of this risk.

Prepare a discounted cash flow analysis to determine whether your employer should implement this capital project. Your analysis should reveal answers to each of the following questions. Clearly label all cells. Highlight the cells that answer the following questions:

1. What is the initial investment amount (Year 0)?
2. What are the total cash flows each year (Years 1-5)
3. What is the NPV?
4. What is the IRR?

R.A.T.-Create Your Own Water Park Apply your knowledge of polynomial functions to create a water park, with 6 waterslides - one for under 6 years old (highest point at least 5m above ground) two for ages 6 to 12 (highest point at least 10m above ground) three for over age 12 (highest point at least 20 m above ground)

A Create a polynomial equation for each waterslide. Show all of your work. The waterslide must begin at the y axis and the x axis must represent the ground. For each function, write the original function in factored form, then explain the transformations that were performed, in order to obtain the model function.

B. Graph (and print) each function using desmos. State the domain and range of each function.

C. Choose one of your waterslides and determine the interval(s) in which the height of the ride was above 3m. Explain your method.

D. Choose one of the waterslides for ages 12 and up and state the interval (from peak to trough) where the waterslide is steepest. Then determine the average rate of change for that interval (by using the equation). Next, determine the instantaneous rate of change at the point in the interval when the person is moving the quickest. Interpret the meaning of these numbers. Note: the maximum steepness of a ride should not exceed 4:1, rise to run. The waterslide should be decelerating as it comes to a stop.

1. Define “Noise Factor”.

2. In an RF receiver system with cascaded amplifiers, where should most of the RF amplification take place, near the antenna or near the output? Why?

The state of California has a mean annual rainfall of 22 inches, whereas the state of New York has a mean annual rainfall of 42 inches. Assume that the standard deviation for both states is 4 inches. A sample of 34 years of rainfall for California and a sample of 46 years of rainfall for New York has been taken.

(a)

Show the probability distribution of the sample mean annual rainfall for California.

A bell-shaped curve is above a horizontal axis labeled inches.

• The horizontal axis ranges from about −2.1 to about 2.1.
• The curve enters the viewing window near −2.1 just above the horizontal axis, curves up to the right, and reaches a maximum near 0.
• The curve then curves down and to the right until it leaves the viewing window at the same height it entered near 2.1.

A bell-shaped curve is above a horizontal axis labeled inches.

• The horizontal axis ranges from about 39.9 to about 44.1.
• The curve enters the viewing window near 39.9 just above the horizontal axis, curves up to the right, and reaches a maximum near 42.
• The curve then curves down and to the right until it leaves the viewing window at the same height it entered near 44.1.

A bell-shaped curve is above a horizontal axis labeled inches.

• The horizontal axis ranges from about 19.9 to about 24.1.
• The curve enters the viewing window near 19.9 just above the horizontal axis, curves up to the right, and reaches a maximum near 22.
• The curve then curves down and to the right until it leaves the viewing window at the same height it entered near 24.1.

A bell-shaped curve is above a horizontal axis labeled inches.

• The horizontal axis ranges from about 10 to about 34.
• The curve enters the viewing window near 10 just above the horizontal axis, curves up to the right, and reaches a maximum near 22.
• The curve then curves down and to the right until it leaves the viewing window at the same height it entered near 34.

(b)

What is the probability that the sample mean is within 1 inch of the population mean for California? (Round your answer to four decimal places.)

(c)

What is the probability that the sample mean is within 1 inch of the population mean for New York? (Round your answer to four decimal places.)

(d)

In which case, part (b) or part (c), is the probability of obtaining a sample mean within 1 inch of the population mean greater? Why?

part (c), because the population standard deviation is smallerpart (c), because the sample size is larger    part (b), because the standard error is smallerpart (b), because the population standard deviation is smaller