Consider a sharp crested (uncontracted horizontal) rectangular weir 1.0 m long and 0.8 m high. The channel receives a flow of 0.3 m3 /sec. What will be the depth and velocity in the channel?

The following are distances (in miles) traveled to the workplace by 17 employees of a certain hospital.

What is The 25^th percentile?

What is the 70th percentile?

For a satellite at a height of 25,000 miles, at what speed must the satellite be traveling to achieve a circular orbit? (A score of 100% will tell you that you have achieved a circular orbit).

The analytics department of a public transit service group is trying to forecast the future number of passengers using the University subway station during the Fall term. During the first 10 days of September, the team count the number of passengers entering and exiting the station between 8:00am to 10:00pm.
Day   # Passengers
1   2250
2   2100
3   2150
4   2450
5   2250
6   2500
7   2300
8   2650
9   2350
10   2600

a)   Compute manually (show your formulas) the forecast for days 1-4 using the exponential smoothing method with an alpha of 0.3.
b)   Now switch to Excel and compute the exponential smoothing forecasts for days 11 and 12 (again using an alpha of 0.3). (Show your Excel Formulas)
c)   Reforecast days 11 and 12 using an alpha of 0.7.
d)   Compare how well the model forecast for periods 8-10 for alpha = 0.3 vs alpha =0.7. Which one was better? Explain.

Kate recently invested in real estate with the intention of selling the property one year from today. She has modeled the returns on that investment based on three economic scenarios. She believes that if the economy stays healthy, then her investment will generate a 30 percent return. However, if the economy softens, as predicted, the return will be 10 percent, while the return will be -25 percent if the economy slips into a recession.

1) If the probabilities of the healthy, soft, and recessionary states are 0.6 , 0.3 , and 0.1 , respectively, then calculate the coefficient of variation for the investment?

2) Barbara is considering investing in a stock and is aware that the return on that investment is particularly sensitive to how the economy is performing. Her analysis suggests that four states of the economy can affect the return on the investment. Using the table of returns and probabilities below calculate the coefficient of variation for the investment?

3) Ben would like to invest in gold and is aware that the returns on such an investment can be quite volatile. Use the following table of states, probabilities, and returns and calculate the coefficient of variation for the investment?

EXPECTED RETURN

A stock's returns have the following distribution:

1. Calculate the stock's expected return. Round your answer to two decimal places.
   %

2. Calculate the stock's standard deviation. Do not round intermediate calculations. Round your answer to two decimal places.
   %

3. Calculate the stock's coefficient of variation. Round your answer to two decimal places.

EXPECTED RETURNS

Stocks A and B have the following probability distributions of expected future returns:

1. Calculate the expected rate of return, r_B, for Stock B (r_A = 9.90%.) Do not round intermediate calculations. Round your answer to two decimal places.
   %

2. Calculate the standard deviation of expected returns, σ_A, for Stock A (σ_B = 27.01%.) Do not round intermediate calculations. Round your answer to two decimal places.
   %

3. Now calculate the coefficient of variation for Stock B. Round your answer to two decimal places.

In each of parts​ (a)-(c), we have given a likely range for the observed value of a sample proportion p. Based on the given​ range, identify the educated guess that should be used for the observed value of p to calculate the required sample size for a prescribed confidence level and margin of error.

a. 0.2 to 0.3

b. 0.1 or less

c. 0.3 or greater

Using all the data below, construct an empirical model using a computational tool (matlab, or R, any preferred). explain your model.

Data Description: These data are from a NIST study involving calibration of ozone monitors. The response variable (y) is the customer's measurement of ozone concentration and the predictor variable (x) is NIST's measurement of ozone concentration. MATLAB Row Vectors: xLst = [0.2, 337.4, 118.2, 884.6, 10.1, 226.5, 666.3, 996.3, 448.6, 777.0, 558.2, 0.4, 0.6, 775.5, 666.9, 338.0, 447.5, 11.6, 556.0, 228.1, 995.8, 887.6, 120.2, 0.3, 0.3, 556.8, 339.1, 887.2, 999.0, 779.0, 11.1, 118.3, 229.2, 669.1, 448.9, 0.5];

yLst = [0.1, 338.8, 118.1, 888.0, 9.2, 228.1, 668.5, 998.5, 449.1, 778.9, 559.2, 0.3, 0.1, 778.1, 668.8, 339.3, 448.9, 10.8, 557.7, 228.3, 998.0, 888.8, 119.6, 0.3, 0.6, 557.6, 339.3, 888.0, 998.5, 778.9, 10.2, 117.6, 228.9, 668.4, 449.2, 0.2];

1. Consider two farmers, one who owns land and the other who rents it from someone else. In good times (which happen with probability 0.3), the owner-farmer earns an income of 125. In bad times (which happen with probability 0.7), he earns an income of 75. The tenant works on a farm that is twice as large and earns an income of 250 in good times (prob=0.3) and 150 in bad times (prob=0.7).

   1. However, he must pay a rent of 100. Calculate the expected net income of both farmers.

   2. Assume that their utility function takes the following form: ? = ?1/2, where ?stands for the farmer’s net income. Calculate the expected utility of both.

   3. Compare this result to the calculation on expected income. What do you conclude in terms of the different risks that both farmers face?

The accompanying table provides data for​ tar, nicotine, and carbon monoxide​ (CO) contents in a certain brand of cigarette. Find the best regression equation for predicting the amount of nicotine in a cigarette. Why is it​ best? Is the best regression equation a good regression equation for predicting the nicotine​ content? Why or why​ not?

1. Find the best regression equation for predicting the amount of nicotine in a cigarette. Use predictor variables of tar​ and/or carbon monoxide​ (CO). Select the correct choice and fill in the answer boxes to complete your choice. ​(Round to three decimal places as​ needed.)

A. Nicotine = ____ + (____) CO

B. Nicotine = ____ + (____) Tar

C. Nicotine = ____ + (____) Tar + (____) CO

2. Why is this equation best?

A. It is the best equation of the three because it has the lowest adjusted R2​, the highest​ P-value, and only a single predictor variable.

B. It is the best equation of the three because it has the highest adjusted R2 the lowest​ P-value, and only a single predictor variable.

C. It is the best equation of the three because it has the lowest adjusted R2​, the highest​ P-value, and removing either predictor noticeably decreases the quality of the model.

D. It is the best equation of the three because it has the highest adjusted R2​, the lowest​ P-value, and removing either predictor noticeably decreases the quality of the model.

3. Is the best regression equation a good regression equation for predicting the nicotine​ content? Why or why​ not?

A. ​No, the large​ P-value indicates that the model is not a good fitting model and predictions using the regression equation are unlikely to be accurate.

B. Yes, the small​ P-value indicates that the model is a good fitting model and predictions using the regression equation are likely to be accurate.

C. No, the small​ P-value indicates that the model is not a good fitting model and predictions using the regression equation are unlikely to be accurate.

D. ​Yes, the large​ P-value indicates that the model is a good fitting model and predictions using the regression equation are likely to be accurate.