Statistic

Q4 (a) On a sunny day, a theme park had 1,000 visitors. According to the attendance record, 800 visitors took a ride on the roller coaster; 450 visitors took a ride on the merry-go-round. It is estimated that among those visitors who took a ride on the roller coaster, 40% of them also took a ride on the merry-go-round. A visitor on that day is selected at random.

i. What is the probability that this visitor rode on both rides?

ii. What is the probability that this visitor rode on no rides at all?

iii. If this visitor has taken a ride on the merry-go-round, what is the probability that he has not ridden on the roller coaster?

Q4(b) In a tutorial session, there are 11 Japanese students, 6 American students and 8 Australian students. Among these 25 students, a group of 5 students is selected randomly for the first presentation.

i. How many different groups can be formed?

ii. What is the probability that this group consists of only Japanese students?

iii. What is the probability that this group consists of exactly 2 Japanese students and 3 American students?

Q4(c) Three urns contain colored balls. Urn 1 contains 3 red, 4 white and 1 blue balls. Urn 2 contains 4 red, 3 white and 2 blue balls. Urn 3 contains 1 red, 2 white and 3 blue balls. One urn is chosen at random and a ball is drawn from it. If the ball is red, what is the probability that it came from Urn 3?

3. You are the CFO of a company looking to build a new office park beginning five years from now.
You will need $2M to purchase land at that time and immediately hypothecate the parcel to stand for
a 24-month, straight (non-amortizing) construction loan of $1.5M @ 7%. Also at that time you will
pay a half point commitment fee to the take-out lender. Upon completion (seven years from now), the
take-out lender will take over the construction loan balance ($1.5M) for a 20-year, 5%, level monthly
payment fully amortized mortgage.

a. How much will you have to set aside each quarter beginning three months from now in MMF
earning 1%/qtr. to have the necessary funds available to purchase the parcel and pay the commitment
fee?

b. You anticipate either selling the building or refinancing it after 10 years. How much will the
balance be on the mortgage at the halfway point?

EuroDisney opened in 1992, but unlike the American version, the theme park was a financial bust. Why?

Select one:

a. Disney made the incorrect assumptions about the size of the pool of European travellers and tourists comprising market demand.

b. They had difficulty hiring and training skilled staff resulting in poor customer service and bad word-of-mouth advertising.

c. Disney assumed the attractions featured in America would be equally exciting to European travellers because many European travelers came to America to visit our theme parks.

d. Although Disney attracted enough visitors, the value of the dollar versus the Euro caused the park to show numerous financial losses.

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A marketing dashboard is a collection of pertinent parts of company scorecards known as metrics that measure marketing performance.

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True

False

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A company that creates a broad plan that identifies its most promising markets and analyzes competitor solutions and market opportunities has developed what kind of plan?

Select one:

a. Operational Plan

b. Strategic Plan

c. Functional Plan

d. Marketing Plan

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The first task of a marketing plan for a company with a Mission is to evaluate the organization's business environment including its potential opportunities and threats.

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True

False

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AARP is a very good direct marketing company. So when the marketing manager became concerned that AARP products and services were not selling as well to the upcoming generation of senior citizens (the Baby Boom generation) compared to prior generations, she employed a market researcher to analyze responses to AARP's recent test marketing of different product offerings directed to Baby Boomers. Based on one of the answers below, it is clear that the researcher didn't understand the research problem that the marketer wanted addressed by the research project. Which of these conclusions from the researcher would indicate that the marketer and the researcher had a misunderstanding of the research problem?

Select one:

a.

b.

c.

d.

16. A county is considering using a piece of park land for one of two alternative projects. Project A would require construction costs of $180,000 (year 0) and generate net benefits of $35,000 per year for 8 years. (The benefits are realized at the ends of years 1 through 8). Project B would require construction costs of $2.25 million and generate net benefits of $150,000 per year for 24 years. (The benefits are realized at the ends of years 1 through 24). Each project is assumed to have zero salvage value at the end of its life.  If these figures are in real dollars, and the real discount rate is 6 percent, which project would the county select? Show your calculations - you can upload your Excel calculations. (You will have to calculate the NPV of each project then use the EANB or Roll-over method to compare the two projects of different life spans).

An amusement park studied methods for decreasing the waiting time (minutes) for rides by loading and unloading riders more efficiently. Two alternative loading/unloading methods have been proposed. To account for potential differences due to the type of ride and the possible interaction between the method of loading and unloading and the type of ride, a factorial experiment was designed. Use the following data to test for any significant effect due to the loading and unloading method, the type of ride, and interaction. Use = .05. Factor A is method of loading and unloading; Factor B is the type of ride. Type of Ride Roller Coaster Screaming Demon Long Flume Method 1 45 55 53 47 47 49 Method 2 52 55 51 54 51 47 Set up the ANOVA table (to 2 decimal, if necessary). Round p-value to four decimal places. Source of Variation Sum of Squares Degrees of Freedom Mean Square F p-value Factor A Factor B Interaction Error Total The p-value for Factor A is What is your conclusion with respect to Factor A? The p-value for Factor B is What is your conclusion with respect to Factor B? The p-value for the interaction of factors A and B is What is your conclusion with respect to the interaction of Factors A and B? What is your recommendation to the amusement park?

Sam and Ryan stand at some distances apart in a park, each making sound with an identical 512Hz tuning fork. A bird resting at the midpoint between them detects a sound of intensity level of 40dB, assume this bird has a threshold of hearing of 10^-14 w/m², (I) what is the pressure amplitude of the sound wave from each tuning fork? (II) If the power output of each tuning fork is 10^-6 W, how far apart are Sam and Ryan ? (III) The bird is now flying away. When the bird is 1 km from Sam, the intensity drops to 10 dB, how far is the bird from Ryan?

An amusement park ride consists of a cylindrical chamber of radius R that can rotate. The riders stand along the wall and the chamber begins to rotate. Once the chamber is rotating fast enough (at a constant speed), the floor of the ride drops away and the riders remain "stuck" to the wall. The coefficients of friction between the rider and the wall are us and uk. 1. Draw a free body diagram of a rider of mass m after the floor has fallen away. 2. Is the rider on the wall accelerating? If so, in what direction? Should our FBD be balanced? 3. Write Newton's second law in the vertical direction. 4. Write Newton's second law in the horizontal direction. 5. If the ride takes a time T to go through one full revolution, what is the speed of the rider on the wall of the ride? 6. Assume that the ride is spinning just fast enough to keep the rider on the wall. Using the equations found in questions #3 and #4, calculate the minimum velocity to keep the rider suspended. 7. You get on the ride and notice another rider beside you who has twice your mass. If the ride is going just fast enough to keep you suspended, will the person beside you have a problem on the ride? 8. After a rider gets sick on the ride, the operator hoses down the walls of the ride, which reduces the coefficient of friction by half. What happens to the minimum velocity required for the rider to remain suspended?

An amusement park studied methods for decreasing the waiting time (minutes) for rides by loading and unloading riders more efficiently. Two alternative loading/unloading methods have been proposed. To account for potential differences due to the type of ride and the possible interaction between the method of loading and unloading and the type of ride, a factorial experiment was designed. Use the following data to test for any significant effect due to the loading and unloading method, the type of ride, and interaction. Use . Factor A is method of loading and unloading; Factor B is the type of ride.

Set up the ANOVA table (to whole number, but -value to 2 decimals and  value to 1 decimal, if necessary).

An amusement park studied methods for decreasing the waiting time (minutes) for rides by loading and unloading riders more efficiently. Two alternative loading/unloading methods have been proposed. To account for potential differences due to the type of ride and the possible interaction between the method of loading and unloading and the type of ride, a factorial experiment was designed. Use the following data to test for any significant effect due to the loading and unloading method, the type of ride, and interaction. Use  = .05. Factor A is method of loading and unloading; Factor B is the type of ride.

1. Set up the ANOVA table (to 2 decimal, if necessary). Round p-value to four decimal places.
   

   Source of Variation	Sum of Squares	Degrees of Freedom	Mean Square	F	p-value
   Factor A
   Factor B
   Interaction
   Error
   Total

   
   
2. The p-value for Factor A is Select:less than .01, between .01 and .025, between .025 and .05, between .05 and .10, greater than .10
3. What is your conclusion with respect to Factor A? Select:Factor A is significant, Factor A is not significant
4. The p-value for Factor B is Select: less than .01, between .01 and .025 between .025 and .05, between .05 and .10, greater than .10
5. What is your conclusion with respect to Factor B?
   Select: Factor B is significant, Factor B is not significant
   
6. The p-value for the interaction of factors A and B is Select: less than .01, between .01 and .025, between .025 and .05, between .05 and .10, greater than .10
7. What is your conclusion with respect to the interaction of Factors A and B?
   Select: The interaction of factors A and B is significant, The interaction of factors A and B is not significantI
   
8. What is your recommendation to the amusement park?
   Select: Use method 1; it has a lower sample mean waiting time and is the best method, Withhold judgment; take a larger sample before making a final decision Since method is not a significant factor, use either loading and unloading method

In a city park a nonuniform wooden beam 9.00 m long is suspended horizontally by a light steel cable at each end. The cable at the left-hand end makes an angle of 30.0∘ with the vertical and has tension 630 N. The cable at the right-hand end of the beam makes an angle of 50.0∘ with the vertical.

a) As an employee of the Parks and Recreation Department, you are asked to find the weight of the beam.

b) Find the location of its center of gravity.