SCM 366

Revenue Management Assignment II

II. San Francisco Express Airlines, SaFE for short, flies from PHL to SFO. On a Thursday evening flight, the number of last-minute no-shows and cancellations is Poisson distributed with mean 7.5. SaFE has an unlimited number of low fare travelers who pay $300. The cost of bumping such a passenger is estimated to be $350 (due lost goodwill as well as the cost of routing their itinerary through other airlines).   SaFE offers this low fare because it also comes with a cancellation/rebooking fee of $150 – if a customer doesn’t show up for the flight or cancels her reservation, she must pay $150 to use the ticket on another flight.

To maximize revenue from this flight, how many seats should the airline overbook?

Customers are more reliable on the Friday evening flight. On that flight, the average number of no-shows and cancellations is Poisson with mean 4.5. Suppose SaFE overbooks that flight by 6 seats. What is the probability that at least 1 passenger will be bumped from this flight?

PLEASE ANSWER IT IN EXCEL SHEET WITH EXPLANATION

The latest political survey in the United States indicates that, of randomly chosen citizens, the probability that they are liberal is 0.22, the probability that they are conservative is 0.55, and the probability that they are neither one nor another is 0.24. Assuming these probabilities are accurate, answer the following questions regarding the group of 10 randomly chosen Americans. (16 point)
What is the probability that four are liberal?
What is the probability that neither is conservative?
What is the probability that two are neither?
What is the probability that at least eight are liberals?

1. Two golf balls are selected with replacement from a bowl containing 7 red and 3 blue balls
   1. What is the probability that both balls are red?
   2. What is the probability that both balls are blue?
   3. What is the probability that the first ball is red and the second ball is blue?
   4. What is the probability that the first ball is blue and the second ball is red?
   5. What is the probability that the two balls selected are the same color?
2. Adam goes to the grocery store. Suppose probability he buys milk is 40%, and the probability he buys steak is 70%, and the probability of both is 30%. What is the probability that he buys either milk or steak?
3. A car dealer has had issues with new cars that are being delivered with flawed paint and tires that are one too small. The two assembly shops are not related to one another. If the probability of flawed paint is 5% and the probability of the wrong size tire is 8%, then what is the probability that the next car delivered will have flawed paint and too small tires?

Allen's hummingbird (Selasphorus sasin) has been studied by zoologist Bill Alther.† Suppose a small group of 10 Allen's hummingbirds has been under study in Arizona. The average weight for these birds is x = 3.15 grams. Based on previous studies, we can assume that the weights of Allen's hummingbirds have a normal distribution, with σ = 0.32 gram.

(a) Find an 80% confidence interval for the average weights of Allen's hummingbirds in the study region. What is the margin of error? (Round your answers to two decimal places.)

(b) What conditions are necessary for your calculations? (Select all that apply.)

σ is unknownnormal distribution of weightsσ is knownn is largeuniform distribution of weights

(c) Interpret your results in the context of this problem.

There is an 80% chance that the interval is one of the intervals containing the true average weight of Allen's hummingbirds in this region.There is a 20% chance that the interval is one of the intervals containing the true average weight of Allen's hummingbirds in this region.     The probability that this interval contains the true average weight of Allen's hummingbirds is 0.20.The probability to the true average weight of Allen's hummingbirds is equal to the sample mean.The probability that this interval contains the true average weight of Allen's hummingbirds is 0.80.

(d) Find the sample size necessary for an 80% confidence level with a maximal margin of error  E = 0.08 for the mean weights of the hummingbirds. (Round up to the nearest whole number.)
hummingbirds

Allen's hummingbird (Selasphorus sasin) has been studied by zoologist Bill Alther.† Suppose a small group of 16 Allen's hummingbirds has been under study in Arizona. The average weight for these birds is x = 3.15 grams. Based on previous studies, we can assume that the weights of Allen's hummingbirds have a normal distribution, with σ = 0.24 gram.

(a) Find an 80% confidence interval for the average weights of Allen's hummingbirds in the study region. What is the margin of error? (Round your answers to two decimal places.)

(b) What conditions are necessary for your calculations? (Select all that apply.)

σ is unknown n is large uniform distribution of weights normal distribution of weights σ is known

(c) Interpret your results in the context of this problem.

There is an 80% chance that the interval is one of the intervals containing the true average weight of Allen's hummingbirds in this region. The probability to the true average weight of Allen's hummingbirds is equal to the sample mean.     The probability that this interval contains the true average weight of Allen's hummingbirds is 0.20. There is a 20% chance that the interval is one of the intervals containing the true average weight of Allen's hummingbirds in this region. The probability that this interval contains the true average weight of Allen's hummingbirds is 0.80.

(d) Find the sample size necessary for an 80% confidence level with a maximal margin of error E = 0.15 for the mean weights of the hummingbirds. (Round up to the nearest whole number.)

Allen's hummingbird (Selasphorus sasin) has been studied by zoologist Bill Alther.† Suppose a small group of 14 Allen's hummingbirds has been under study in Arizona. The average weight for these birds is x = 3.15 grams. Based on previous studies, we can assume that the weights of Allen's hummingbirds have a normal distribution, with ? = 0.38 gram.

(a) Find an 80% confidence interval for the average weights of Allen's hummingbirds in the study region. What is the margin of error? (Round your answers to two decimal places.)

(b) What conditions are necessary for your calculations? (Select all that apply.)

uniform distribution of weights? is unknownn is largenormal distribution of weights? is known

(c) Interpret your results in the context of this problem.

There is an 80% chance that the interval is one of the intervals containing the true average weight of Allen's hummingbirds in this region.The probability that this interval contains the true average weight of Allen's hummingbirds is 0.80.     The probability that this interval contains the true average weight of Allen's hummingbirds is 0.20.There is a 20% chance that the interval is one of the intervals containing the true average weight of Allen's hummingbirds in this region.The probability to the true average weight of Allen's hummingbirds is equal to the sample mean.

(d) Find the sample size necessary for an 80% confidence level with a maximal margin of error  E = 0.06 for the mean weights of the hummingbirds. (Round up to the nearest whole number.)
hummingbirds

A smallsample ofUWIstudents were asked whethertheywere in favor of or against abortion. Some information about these students is shownbelow.

a. how many elements are in the data set?

b. How many variables are in the data set

c. which of the variables are categorical and which are quantitative

2 Asurvey of a sample of business students resulted in the following information regarding the genders of the individuals and their selected major.

a. What is the probability of selectingan individual who is majoringinMarketing?

b. What is the probability of selecting a female?

c. Whatistheprobability ofselecting a femalewhoisalsomajoring in Management?

d. Whatistheprobabilityofselectinganindividualwhoismajoring in Management, given that the person isfemale?

e. What is the probability of selecting a female OR a management Major.

f. Are the events “Female” and “Management ” mutually exclusive? Explain using probabilities

g. Are the events “Female” and “Management ” independent events? Explain using probabilities.

Allen's hummingbird (Selasphorus sasin) has been studied by zoologist Bill Alther.† Suppose a small group of 18 Allen's hummingbirds has been under study in Arizona. The average weight for these birds is x = 3.15 grams. Based on previous studies, we can assume that the weights of Allen's hummingbirds have a normal distribution, with σ = 0.32 gram.

(a) Find an 80% confidence interval for the average weights of Allen's hummingbirds in the study region. What is the margin of error? (Round your answers to two decimal places.)

(b) What conditions are necessary for your calculations? (Select all that apply.)

uniform distribution of weights

normal distribution of weights

σ is known

n is large

σ is unknown

(c) Interpret your results in the context of this problem.

The probability that this interval contains the true average weight of Allen's hummingbirds is 0.80.

The probability to the true average weight of Allen's hummingbirds is equal to the sample mean.    

There is an 80% chance that the interval is one of the intervals containing the true average weight of Allen's hummingbirds in this region.

The probability that this interval contains the true average weight of Allen's hummingbirds is 0.20.

There is a 20% chance that the interval is one of the intervals containing the true average weight of Allen's hummingbirds in this region.

(d) Find the sample size necessary for an 80% confidence level with a maximal margin of error E = 0.06 for the mean weights of the hummingbirds. (Round up to the nearest whole number.)
____________________ hummingbirds