1. An airport limousine can accommodate up to 4 passengers on any one trip. The company will accept a maximum of 6 reservations for a trip, and a passenger must have a reservation. From previous records, 20% of all those making reservations do not show up for the trip. Answer the following questions assuming independence wherever appropriate.

   A) Assume that six reservations are made. Let X = the number of customers who have made a reservation and show up for the trip. Find the probability distribution function of X in table form.
2. B)Assume that six reservations are made. What is the probability that at least one individual with a reservation shows cannot be accommodated on the trip?
3. C)Assume that six reservations are made. What is the expected number of available places when the limousine departs?
4. Suppose that the probability distribution of the number of reservations made is given by the accompanying table. Let Y denote the number of passengers on a randomly selected trip.
5. D) Obtain the probability distribution function of Y in table form.The possible values for Y are 0, 1, 2, 3, 4. You are still assuming that 20% of passengers who have made a reservation do not show up.
6. E) Find the expected value of Y.

There are two traffic lights on a commuter's route to and from work. Let X₁ be the number of lights at which the commuter must stop on his way to work, and X₂ be the number of lights at which he must stop when returning from work. Suppose that these two variables are independent, each with the pmf given in the accompanying table (so X₁, X₂ is a random sample of size n = 2).

(a) Determine the pmf of T_o = X₁ + X₂.

(b) Calculate μ_To.
μ_To =

How does it relate to μ, the population mean?
μ_To =  · μ

(c) Calculate σ_To².

How does it relate to σ², the population variance?
σ_To² =  · σ²

(d) Let X₃ and X₄ be the number of lights at which a stop is required when driving to and from work on a second day assumed independent of the first day. With T_o = the sum of all four X_i's, what now are the values of E(T_o) and V(T_o)?

(e) Referring back to (d), what are the values of

P(T_o = 8) and P(T_o ≥ 7)

[Hint: Don't even think of listing all possible outcomes!] (Enter your answers to four decimal places.)

A scientist is studying the relationship between x = inches of annual rainfall and y = inches of shoreline erosion. One study reported the following data. Use the following information to solve the problem by hand, then use SPSS output to verify your answers. .

X         30        25        90        60        50        35       75        110      45        80

Y         0.3       0.2       5.0       3.0       2.0       0.5       4.0       6.0       1.5       4.0

a. What is the equation of the estimated regression line?

= ______________

b. Plot the data and graph the line. Does the line appear to provide a good fit to the data points?

c. Use the least-squares line to predict the value of y when x =39

d. Fill in the missing entries in the SPSS analysis of variance table

Source             DF                   SS                    MS                  F                      P

Regression       1                      37.938

Error                ____                _____              0.058               ____________

e) Is the simple linear regression model useful for predicting erosion from a given amount of rainfall?

f) What is the p-value?

g) A linear relationship ______________ exist between x and y.

h) The simple linear regression model ______________ useful for predicting erosion from a given amount of rainfall.

i) What is the coefficient of determination.(r-squared) or r?

j) Interpret the coefficient (r-squared) of determination.

. A bike shop is selling a fashionable newly designed folding bike. The shop is now considering how many of them to order for the coming season. The supplier requires that orders for the bikes must be placed in quantities of 25. The cost per bike is $820, $790, $750 and $700 for an order of 25, 50, 75 and 100 respectively. The bikes will be sold for $1,200 each. Since there will be a new design for folding bikes next season and there is no spare storage space in the store, any bikes left over at the end of this season will have to be sold at a low price of $450 each to another bike shop. However, if the shop runs out of bikes during the season, it will suffer a loss of goodwill among its customers. The shop estimates this goodwill loss to $60 per customer who is not able to buy a bike. From past experience, the shop estimates that the demand for folding bikes this coming season will be 25, 50, 75 and 100 bikes with probabilities of 0.4, 0.3, 0.2 and 0.1 respectively.

(a) Construct the payoff table for the above situation.

(b) Which alternative should be chosen using each of the maximax, maximin, minimax regret, Hurwicz (take α = 0.6), equal likelihood, expected value, and expected opportunity loss criteria?

(c) Find the expected value of perfect information.

Suppose your expectations regarding the stock market are as follows: State of the Economy Probability HPR Boom 0.4 32% Normal growth 0.3 20 Recession 0.3 -16 Use above equations to compute the mean and standard deviation of the HPR on stocks. (Do not round intermediate calculations. Round your answers to 2 decimal places.) Please show all working.

A $1000 bond with a coupon rate of 6.2% paid semiannually has eight years to maturity and a yield to maturity of 8.3%. If interest rates rise and the yield to maturity increases to 8.6%, what will happen to the current yield of the bond?

1. 	A.	The current yield will decrease by 0.129%.
   	B.	The current yield will increase by 0.3%.
   	C.	The current yield will decrease by 0.3%
   	D.	The current yield will increase by 0.129%.

The mean caffeine content μ of a certain energy drink is under examination. A measure taken on a random sample of size n = 16 yieldsx̄ = 2.4 g/l.

1. (a) Assuming that the standard deviation is known to be σ = 0.3, find the 95 confidence interval for μ.

2. (b) If that the standard deviation is unknown but the sample standard deviation is s = 0.3, find the 95 confidence interval for μ.

Describe the externalities associated with a football stadium compared with
an amusement park. Which would have greater positive externalities? Which
would have greater negative externalities?

How can a theme park eliminate waiting in long lines including rides etc. How much will they cost? What resources and expenditures will your solution entail?

Please answer each question in 350-500 words.

If you were running the organization(Hotel Management Group), what changes would you make and why?