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The weight of luggage carried onto a plane by passengers is normally distributed with a mean

of 20 KG and a standard deviation of 6 KG.

a. What is the probability that a passenger's luggage weighs 25 KG?

b. Passengers are "fast-tracked" if they have luggage weighing less than 10 KG. What percentage of

passengers are fast tracked?

c. The airline wants to set the maximum weight limit so that only 2.5% of passengers have to pay an

overweight luggage fee. What limit should it set?

d. If the plane has 100 passengers, what is the probability that the average weight of their luggage is

less than 23 KG?

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Darryn D'Souza
Darryn D'SouzaLv10
28 Sep 2019

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Related questions

The distribution of the baggage weights for passengers using a particular airline has a mean of 20 lbs and a standard deviation of 5 lbs. For a random sample of 100 passengers, what is the probability that ...

a. the total luggage weight is less than 2030 lbs? Give your answer to 4 decimal places.

b. the sample mean weight is within 0.1 lb of the overall mean? That is, what is the probability that the sample mean weight is between 19.9 and 20.1 lbs? Give your answer to 4 decimal places.

c. The probabilities in parts (a) and (b) are exact. (True or False?)

What valuable company is nobody building? This question is harder than it looks, because your company could create a lot of value without becoming very valuable itself. Creating value isn't enough -- you also need to capture some of the value you create. This means that even very big businesses can be bad businesses. For example, U.S. airline companies serve millions of passengers and create hundreds of billions of dollars of value each year. But in 2012, when the average airfare each way was $178, the airlines made only 37 cents per passenger trip. Compare them to Google, which creates less value but captures far more. Google brought in $50 billion in 2012 (versus $160 billion for the airlines), but it kept 21% of those revenues as profits -- more than 100 times the airline industry's profit margin that year. Google makes so much money that it is now worth three times more than every U.S. airline combined. The airlines compete with each other, but Google stands alone. Economists use two simplified models to explain the difference: perfect competition and monopoly. "Perfect competition" is considered both the ideal and the default state in Economics 101. So-called perfectly competitive markets achieve equilibrium when producer supply meets consumer demand. Every firm in a competitive market is undifferentiated and sells the same homogeneous products. Since no firm has any market power, they must all sell at whatever price the market determines. If there is money to be made, new firms will enter the market, increase supply, drive prices down and thereby eliminate the profits that attracted them in the first place. If too many firms enter the market, they'll suffer losses, some will fold, and prices will rise back to sustainable levels. Under perfect competition, in the long run no company makes an economic profit. The opposite of perfect competition is monopoly. Whereas a competitive firm must sell at the market price, a monopoly owns its market, so it can set its own prices. Since it has no competition, it produces at the quantity and price combination that maximizes its profits. To an economist, every monopoly looks the same, whether it deviously eliminates rivals, secures a license from the state or innovates its way to the top. I'm not interested in illegal bullies or government favorites: By "monopoly," I mean the kind of company that is so good at what it does that no other firm can offer a close substitute. Google is a good example of a company that went from 0 to 1: It hasn't competed in search since the early 2000s, when it definitively distanced itself from Microsoft and Yahoo! Americans mythologize competition and credit it with saving us from socialist bread lines. Actually, capitalism and competition are opposites. Capitalism is premised on the accumulation of capital, but under perfect competition, all profits get competed away. The lesson for entrepreneurs is clear: If you want to create and capture lasting value, don't build an undifferentiated commodity business. How much of the world is actually monopolistic? How much is truly competitive? It is hard to say because our common conversation about these matters is so confused. To the outside observer, all businesses can seem reasonably alike, so it is easy to perceive only small differences between them. But the reality is much more binary than that. There is an enormous difference between perfect competition and monopoly, and most businesses are much closer to one extreme than we commonly realize. The confusion comes from a universal bias for describing market conditions in self-serving ways: Both monopolists and competitors are incentivized to bend the truth. Monopolists lie to protect themselves. They know that bragging about their great monopoly invites being audited, scrutinized and attacked. Since they very much want their monopoly profits to continue unmolested, they tend to do whatever they can to conceal their monopoly -- usually by exaggerating the power of their (nonexistent) competition. Think about how Google talks about its business. It certainly doesn't claim to be a monopoly. But is it one? Well, it depends: a monopoly in what? Let's say that Google is primarily a search engine. As of May 2014, it owns about 68% of the search market. (Its closest competitors, Microsoft and Yahoo!, have about 19% and 10%, respectively.) If that doesn't seem dominant enough, consider the fact that the word "google" is now an official entry in the Oxford English Dictionary -- as a verb. Don't hold your breath waiting for that to happen to Bing. But suppose we say that Google is primarily an advertising company. That changes things. The U.S. search-engine advertising market is $17 billion annually. Online advertising is $37 billion annually. The entire U.S. advertising market is $150 billion. And global advertising is a $495 billion market. So even if Google completely monopolized U.S. search-engine advertising, it would own just 3.4% of the global advertising market. From this angle, Google looks like a small player in a competitive world. What if we frame Google as a multifaceted technology company instead? This seems reasonable enough; in addition to its search engine, Google makes dozens of other software products, not to mention robotic cars, Android phones and wearable computers. But 95% of Google's revenue comes from search advertising; its other products generated just $2.35 billion in 2012 and its consumer-tech products a mere fraction of that. Since consumer tech is a $964 billion market globally, Google owns less than 0.24% of it -- a far cry from relevance, let alone monopoly. Framing itself as just another tech company allows Google to escape all sorts of unwanted attention. Non-monopolists tell the opposite lie: "We're in a league of our own." Entrepreneurs are always biased to understate the scale of competition, but that is the biggest mistake a startup can make. The fatal temptation is to describe your market extremely narrowly so that you dominate it by definition. Suppose you want to start a restaurant in Palo Alto that serves British food. "No one else is doing it," you might reason. "We'll own the entire market." But that is only true if the relevant market is the market for British food specifically. What if the actual market is the Palo Alto restaurant market in general? And what if all the restaurants in nearby towns are part of the relevant market as well? These are hard questions, but the bigger problem is that you have an incentive not to ask them at all. When you hear that most new restaurants fail within one or two years, your instinct will be to come up with a story about how yours is different. You'll spend time trying to convince people that you are exceptional instead of seriously considering whether that is true. It would be better to pause and consider whether there are people in Palo Alto who would rather eat British food above all else. They may well not exist. In 2001, my co-workers at PayPal and I would often get lunch on Castro Street in Mountain View, Calif. We had our pick of restaurants, starting with obvious categories like Indian, sushi and burgers. There were more options once we settled on a type: North Indian or South Indian, cheaper or fancier, and so on. In contrast to the competitive local restaurant market, PayPal was then the only email-based payments company in the world. We employed fewer people than the restaurants on Castro Street did, but our business was much more valuable than all those restaurants combined. Starting a new South Indian restaurant is a really hard way to make money. If you lose sight of competitive reality and focus on trivial differentiating factors -- maybe you think your naan is superior because of your great-grandmother's recipe -- your business is unlikely to survive. The problem with a competitive business goes beyond lack of profits. Imagine you're running one of those restaurants in Mountain View. You're not that different from dozens of your competitors, so you've got to fight hard to survive. If you offer affordable food with low margins, you can probably pay employees only minimum wage. And you'll need to squeeze out every efficiency: That is why small restaurants put Grandma to work at the register and make the kids wash dishes in the back. A monopoly like Google is different. Since it doesn't have to worry about competing with anyone, it has wider latitude to care about its workers, its products and its impact on the wider world. Google's motto -- "Don't be evil" -- is in part a branding ploy, but it is also characteristic of a kind of business that is successful enough to take ethics seriously without jeopardizing its own existence. In business, money is either an important thing or it is everything. Monopolists can afford to think about things other than making money; non-monopolists can't. In perfect competition, a business is so focused on today's margins that it can't possibly plan for a long-term future. Only one thing can allow a business to transcend the daily brute struggle for survival: monopoly profits. So a monopoly is good for everyone on the inside, but what about everyone on the outside? Do outsize profits come at the expense of the rest of society? Actually, yes: Profits come out of customers' wallets, and monopolies deserve their bad reputation -- but only in a world where nothing changes. In a static world, a monopolist is just a rent collector. If you corner the market for something, you can jack up the price; others will have no choice but to buy from you. Think of the famous board game: Deeds are shuffled around from player to player, but the board never changes. There is no way to win by inventing a better kind of real-estate development. The relative values of the properties are fixed for all time, so all you can do is try to buy them up. But the world we live in is dynamic: We can invent new and better things. Creative monopolists give customers more choices by adding entirely new categories of abundance to the world. Creative monopolies aren't just good for the rest of society; they're powerful engines for making it better. Even the government knows this: That is why one of its departments works hard to create monopolies (by granting patents to new inventions) even though another part hunts them down (by prosecuting antitrust cases). It is possible to question whether anyone should really be awarded a monopoly simply for having been the first to think of something like a mobile software design. But something like Apple's monopoly profits from designing, producing and marketing the iPhone were clearly the reward for creating greater abundance, not artificial scarcity: Customers were happy to finally have the choice of paying high prices to get a smartphone that actually works. The dynamism of new monopolies itself explains why old monopolies don't strangle innovation. With Apple's iOS at the forefront, the rise of mobile computing has dramatically reduced Microsoft's decadeslong operating system dominance. Before that, IBM's hardware monopoly of the 1960s and '70s was overtaken by Microsoft's software monopoly. AT&T had a monopoly on telephone service for most of the 20th century, but now anyone can get a cheap cellphone plan from any number of providers. If the tendency of monopoly businesses was to hold back progress, they would be dangerous, and we'd be right to oppose them. But the history of progress is a history of better monopoly businesses replacing incumbents. Monopolies drive progress because the promise of years or even decades of monopoly profits provides a powerful incentive to innovate. Then monopolies can keep innovating because profits enable them to make the long-term plans and finance the ambitious research projects that firms locked in competition can't dream of. So why are economists obsessed with competition as an ideal state? It is a relic of history. Economists copied their mathematics from the work of 19th-century physicists: They see individuals and businesses as interchangeable atoms, not as unique creators. Their theories describe an equilibrium state of perfect competition because that is what's easy to model, not because it represents the best of business. But the long-run equilibrium predicted by 19th-century physics was a state in which all energy is evenly distributed and everything comes to rest -- also known as the heat death of the universe. Whatever your views on thermodynamics, it is a powerful metaphor. In business, equilibrium means stasis, and stasis means death. If your industry is in a competitive equilibrium, the death of your business won't matter to the world; some other undifferentiated competitor will always be ready to take your place. Perfect equilibrium may describe the void that is most of the universe. It may even characterize many businesses. But every new creation takes place far from equilibrium. In the real world outside economic theory, every business is successful exactly to the extent that it does something others cannot. Monopoly is therefore not a pathology or an exception. Monopoly is the condition of every successful business. Tolstoy famously opens "Anna Karenina" by observing: "All happy families are alike; each unhappy family is unhappy in its own way." Business is the opposite. All happy companies are different: Each one earns a monopoly by solving a unique problem. All failed companies are the same: They failed to escape competition.

According to the article above by Peter Thiel do you think perfect competition is best for the economy and for consumers? Why or why not? What does Peter Thiel think about perfect competition versus monopolies?

1. You are given only three quarterly seasonal indices and quarterly seasonally adjusted data for the entire year. What is the raw data value for Q4? Raw data is not adjusted for seasonality.

Quarter Seasonal Index Seasonally Adjusted Data

Q1 .80 295

Q2 .85 299

Q3 1.15 270

Q4 --- 271

2. One model of exponential smoothing will provide almost the same forecast as a liner trend method. What are linear trend intercept and slope counterparts for exponential smoothing?

A. Alpha and Delta

B. Delta and Gamma

C. Alpha and Gamma

D. Standard Deviation and Mean

3. When performing correlation analysis what is the null hypothesis? What measure in Minitab is used to test it and to be 95% confident in the significance of correlation coefficient.

A. Ho: r = .05 p < .5

B. Ho: r = 0 p >.05

C. Ho: r ? 0 p?.05

D. Ho: r = 0 p?.05

In decomposition what does the cycle factor (CF) of .80 represent for a monthly forecast estimate of a Y variable?

A. The estimated value is 80% of the average monthly seasonal estimate.
B. The estimate is .80 of the forecasted Y trend value.
C. The estimated value is .80 of the historical average CMA values.
D. The estimated value has 20% more variation than the average historical Y data values.

5. A Wendy's franchise owner notes that the sales per store has fallen below the stated national Wendy's outlet average of $1,368,000. He asserts a change has occurred that reduced the fast food eating habits of Americans. What is his hypothesis (H1) and what type of test for significance must be applied?

A. H1: u ? $1,368,000 A one-tailed t-test to the left.
B. H1: u = $1,368,000 A two-tailed t-test.
C. H1: u < $1,368,000 A one-tailed t-test to the left.
D. H1: p < $1,368,000 A one-tailed test to the right

6. As the sample size from a population increases, for a given level of significance what happens to the null hypothesis rejection region and size of the t-table value?

A. The rejection region and the t-table value generally gets smaller for sample size below 31.
B. The rejection region gets larger and the t-table value generally gets smaller for sample sizes below 31.
C. The rejection region remains unchanged while the t-table value gets smaller for all sample sizes.
D. The zero mean hypothesis region gets larger and the t-table value gets larger as well for sample sizes below 31.

7. You obtained autocorrelation LBQ value of 18.58 for the 12th lag from a data sample. Are the data significantly correlated at the lag examined or not? You want to be 95% confident in your answer.

A. Yes. The data are significantly correlated through the 12th lag.
B. No. The data are not significantly correlated through the 12th lag.

C. No. Only the 12 lag period is not correlated.

D. You cannot tell since the number of sample observations is not provided.

E. The p-value is above .05 so the data is correlated.

8. Sometimes forecasters get lazy or forgetful and do not check the significance of XY data correlations and use the X variable to forecast Y. What is the result of this?

A. Type 2 error
B. Autocorrelation error
C. Type 3 error
D. Type 1 error

9. Do error measures indicate the statistical significance of forecast model variables?

A. Yes. They move in the same direction as statistical significance.
B. Yes. As error measures decrease the variable significance increases.
C. No They indicate only the magnitude of estimate error.
D. No. They indicate only the statistical significance of a forecast or fitted values.

10. In exponential smoothing what is the weight of the alpha coefficient for a time series data observation from the 3rd previous period if the original alpha value is set at .8?

A. The weight cannot be calculated since the data observation is not given.
B. The weight is zero since the alpha value is set relatively high.
C. .548
D. .0064

11.Given the data series below for variables Y (Monthly Inventory Balance) and X (Monthly Sales) are they significantly correlated at the 95% confidence level and how can you tell?

Ending Inv. Bal. Y

Monthly Sales X

1544

5053

1913

5052

2028

7507

1178

2887

1554

3880

1910

4454

1208

3855

2467

8824

2101

5716

A. Yes. The correlation coefficient is .873 that is greater than .05.
B. Yes. The correlation p-value is .002 which is less than .05.
C. No. The correlation coefficient is above the p-value.
D.No. The correlation p-value is greater than the 95% confidence level.

12. You have forecast the sales for your company for the last 12 months and the forecast residuals are shown below. Are these residuals to be considered random?
Residuals

-24

-348

-892

-62

-378

-489

-342

34

490

23

578

198

A. Yes, since the residuals randomly vary in magnitude.
B. Yes since the residuals are positive and negative and vary in magnitude.
C. No, since the residuals are stationary and vary in magnitude.
D. No, since the residuals indicate positive slope.

13. Given the residuals in problem 12 above what is the RMSE for the forecast?

A. -101.0
B. 411.8
C. 169603
D. 220.1

14. Which form of exponential smoothing can result in a na

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