2.44 Athletes’ salaries. The Montreal Canadiens were founded in 1909 and are the longest continuously operating professional ice hockey team. They have won 24 Stanley Cups, making them one of the most successful professional sports teams of the four major sports of Canada and the United States. The table below gives the salaries of the 2013-14 roster. Provide the team owner with a full description of the distribution of salaries and a brief summary of its most important features. HOCKEY
| Player | Salary | Player | Salary | Player | Salary | ||
|---|---|---|---|---|---|---|---|
| Markov | $5,750,000 | Prust | $2,500,000 | Parros | $950,000 | ||
| Price | $5,750,000 | Emelin | $2,000,000 | Galchenyuk | $925,000 | ||
| Gionta | $5,000,000 | Moen | $1,850,000 | Weber | $900,000 | ||
| Plekanec | $5,000,000 | Bouillon | $1,500,000 | Gallagher | $715,000 | ||
| Bourque | $4,000,000 | Murray | $1,500,000 | White | $700,000 | ||
| Briere | $4,000,000 | Eller | $1,500,000 | Bournival | $690,000 | ||
| Pacioretty | $4,000,000 | Budaj | $1,400,000 | Blunden | $575,000 | ||
| Suban | $3,750,000 | Diaz | $1,250,000 | Nokelainen | $575,000 | ||
| Desharnais | $3,500,000 | Armstrong | $1,000,000 |
2.50 Graduation rates. In Exercise 1.10 (page 32) you were asked to use a stemplot to display the distribution of the percents of on-time high school graduates in the states. Stemplots help you find the five-number summary because they arrange the observations in increasing order. GRADRATE
5 | 9
6 | 23
6 | 788
7 | 112444
7 | 56666777888
8 | 0001122333333344
8 | 6666667783.26 Daily activity. It appears that people who are mildly obese are less active than leaner people. One study looked at the average number of minutes per day that people spend standing or walking. Among mildly obese people, minutes of activity varied according to the N(373,67) distribution. Minutes of activity for lean people had the N(526,107) distribution. Within what limits do the active minutes for about 95% of the people in each group fall? Use the 68-95-99.7 rule.
Mile per gallon. In its Fuel Economy Guide for model year 2014 vehicles, the Enviromental Protection Agency gives data on 1160 vehicles. There are a number of high outliers, mainly hybrid gas-electric vehicles. If we ignore the vehicles identified as outliers, however, the combined city and highway gas mileage of the other 1134 vehicles is approximately Normal with mean 22.2 miles per gallon (mpg) and standard deviation 5.2 mpg. Use this information in exercises 3.35 through 3.37.
3.35 I love my bug! The 2014 Volkswagen Beetle with a four-cylinder 1.8L engine and automatic transmission has a combined gas mileage of 28 mpg. What percent of all vehicles have better gas mileage than the Beetle?
3.36 The top 5%. How high must a 2014 vehicle’s gas mileage be in order to fall in the top 5% of all vehicles?
3.37 The middle half. The quartiles of any distribution are the values with cumulative proportions 0.25 and 0.75. They span the middle half of the distribution. What are the quartiles of the distribution of gas mileage?
3.41 Heights of women. The heights of women aged 20 to 29 follow approximately the N(64.2,2.8) distribution. Men the same age have heights distributed as N(69.4,3.0). What percent of women aged 20 to 29 are taller than the mean height of men aged 20 to 29?
3.42 Weights aren’t Normal. The heights of people of the same sax and similar age follow a Normal distribution reasonably closely. Weights, on the other hand, are not Normally distributed. The weights of women aged 20 to 29 have mean 161.9 pounds and median 149.4 pounds. The first and third quartiles are 126.3 pounds and 181.2 pounds. What can you say about the shape of the weight distribution? Why?