There are three students (Alice, Bill and Roby) applying the scholarships which are evaluated by four professors. Each professor (P1, P2, P3 and P4) gives a score (between 0 and 10) which is then combined into an overall score for each student.
Here are the scores given by the four professors:
P1 gives 8, 6, 3 to Alice, Bill and Roby, respectively;
P2 gives 7, 6, 3 to Alice, Bill and Roby, respectively;
P3 gives 6, 4, 7 to Alice, Bill and Roby, respectively;
P4 gives 4, 9, 7 to Alice, Bill and Roby, respectively.
(1) If each judge's score has equal importance, which student(s) get(s) the highest overall score based on the arithmetic mean?
(2) If the importance for the four professors P1, P2, P3 and P4 are 0.4, 0.3, 0.2 and 0.1, respectively. Which student(s) get(s) the highest overall weighted score based on the weighted arithmetic mean?
(3) If using Borda count, such that a student awards 3 points for first place, 1 point for second place and 0 points for third place, what are the overall scores for the three students?

9.3. Jean Clark is the manager of the Midtown Saveway Grocery Store. She now needs to replenish her supply of strawberries. Her regular supplier can provide as many cases as she wants. However, because these strawberries already are very ripe, she will need to sell them tomorrow and then discard any that remain unsold. Jean estimates that she will be able to sell 10, 11, 12, or 13 cases tomorrow. She can purchase the strawberries for $3 per case and sell them for $8 per case. Jean now needs to decide how many cases to purchase.

Jean has checked the store’s records on daily sales of strawberries. On this basis, she estimates that the prior probabilities are 0.2, 0.4, 0.3, and 0.1 for being able to sell 10, 11, 12, and 13 cases of strawberries tomorrow.

Consider the initial value problem: y0 = 3 + x−y, y(0) = 1 (a) Solve it analytically. (b) Solve it using Euler’s method using step size h = 0.1 and find an approximation to true solution at x = 0.3. (c) What is the error in the Euler’s method at x = 0.3

2. A corporate treasurer is looking to invest about $4 million for 60 days. Commercial

paper rates are a 3.65% discount and CD rates are 3.66%.

a) (0.4’) What is the CP’s bond equivalent yield?

b) (0.3’) What is the CD’s bond equivalent yield?

c) (0.3’) Which is the better investment?

A suburban hotel derives its revenue from its hotel and restaurant operations. The owners are interested in the relationship between the number of rooms occupied on a nightly basis and the revenue per day in the restaurant. Below is a sample of 25 days (Monday through Thursday) from last year showing the restaurant income and number of rooms occupied.

1. Choose the scatter diagram that best fits the data.

• Scatter diagram 1

• Scatter diagram 2

• Scatter diagram 3

2. Determine the coefficient of correlation between the two variables. (Round your answer to 3 decimal places.)

1. c-1. State the decision rule for 0.01 significance level: H₀: ρ ≤ 0; H₁: ρ > 0. (Round your answer to 3 decimal places.)

1. c-2. Compute the value of the test statistic. (Round your answer to 2 decimal places.)

1. c-3. Is it reasonable to conclude that there is a positive relationship between revenue and occupied rooms? Use the 0.01 significance level.

4. What percent of the variation in revenue in the restaurant is accounted for by the number of rooms occupied? (Round your answer to 1 decimal place.)

A suburban hotel derives its revenue from its hotel and restaurant operations. The owners are interested in the relationship between the number of rooms occupied on a nightly basis and the revenue per day in the restaurant. Below is a sample of 25 days (Monday through Thursday) from last year showing the restaurant income and number of rooms occupied.

Determine the coefficient of correlation between the two variables. (Round your answer to 3 decimal places.)

c-1. State the decision rule for 0.025 significance level: H0: ρ ≤ 0; H1: ρ > 0. (Round your answer to 3 decimal places.)

c-2Compute the value of the test statistic. (Round your answer to 2 decimal places.)

c-3. Is it reasonable to conclude that there is a positive relationship between revenue and occupied rooms? Use the 0.025 significance level.

What percent of the variation in revenue in the restaurant is accounted for by the number of rooms occupied? (Round your answer to 1 decimal place.)

A suburban hotel derives its revenue from its hotel and restaurant operations. The owners are interested in the relationship between the number of rooms occupied on a nightly basis and the revenue per day in the restaurant. Below is a sample of 25 days (Monday through Thursday) from last year showing the restaurant income and number of rooms occupied.

1. Choose the scatter diagram that best fits the data.

• Scatter diagram 1

• Scatter diagram 2

• Scatter diagram 3

2. Determine the coefficient of correlation between the two variables. (Round your answer to 3 decimal places.)

Pearson correlation _______

1. c-1. State the decision rule for 0.01 significance level: H₀: ρ ≤ 0; H₁: ρ > 0. (Round your answer to 3 decimal places.)

Reject H0 if t > ________

1. c-2. Compute the value of the test statistic. (Round your answer to 2 decimal places.)

Value of the test statistic ______

4. What percent of the variation in revenue in the restaurant is accounted for by the number of rooms occupied? (Round your answer to 1 decimal place.)

_____ % of the variation in revenue is explained by variation in occupied rooms.

A suburban hotel derives its revenue from its hotel and restaurant operations. The owners are interested in the relationship between the number of rooms occupied on a nightly basis and the revenue per day in the restaurant. Below is a sample of 25 days (Monday through Thursday) from last year showing the restaurant income and number of rooms occupied.

1. Determine the coefficient of correlation between the two variables. (Round your answer to 3 decimal places.)

Pearson Correlation:

2.

c-1. State the decision rule for 0.01 significance level: H₀: ρ ≤ 0; H₁: ρ > 0. (Round your answer to 3 decimal places.)

c-2. Compute the value of the test statistic.

D. What percent of the variation in revenue in the restaurant is accounted for by the number of rooms occupied? (Round your answer to 1 decimal place.)

________% of the variation in revenue is explained by variation in occupied rooms.

A suburban hotel derives its revenue from its hotel and restaurant operations. The owners are interested in the relationship between the number of rooms occupied on a nightly basis and the revenue per day in the restaurant. Below is a sample of 25 days (Monday through Thursday) from last year showing the restaurant income and number of rooms occupied.

a. Choose the scatter diagram that best fits the data.

b. Determine the coefficient of correlation between the two variables. (Round your answer to 3 decimal places.)

1. c-1. State the decision rule for 0.01 significance level: H₀: ρ ≤ 0; H₁: ρ > 0. (Round your answer to 3 decimal places.)

1. c-2. Compute the value of the test statistic. (Round your answer to 2 decimal places.)

1. c-3. Is it reasonable to conclude that there is a positive relationship between revenue and occupied rooms? Use the 0.01 significance level.

d.

4. What percent of the variation in revenue in the restaurant is accounted for by the number of rooms occupied? (Round your answer to 1 decimal place.)