1.23 Medical students. Students who have finished medical school are assigned to residencies in hospitals to receive further training in a medical specialty. Here is part of a hypothetical data base of students seeking residency positions. USMLE is the student's score on Step 1 of the national medical licensing examination.
Name | Medical school | Sex | Age | USMLE | Specialty sought |
---|---|---|---|---|---|
Abrams, Laurie | Florida | F | 28 | 238 | Familty medicine |
Brown, Gordon | Meharry | M | 25 | 205 | Radiology |
Cabrera, Maria | Tufts | F | 26 | 191 | Pediatrics |
Ismael, Miranda | Indiana | F | 32 | 245 | Internal medicine |
1.26 Facebook and MySpace audience Although most social-networking Web sites in the United States have fairly short histories, the growth of these sites has been exponential. By far, the two most visited social-networking sites are Facebook.com and MySpace.com. Here is the age distribution of the audience for the two sites in December 2009. FACEBOOK
1.35 Where are the nurses? The following spreadsheet gives the number of active nurses per 100,000 people in each state. NURSES
2.25 Incomes of college grads. According to the Census Bureau's 2010 Current Population Survey, the mean and median 2009 income of people at least 25 years old who had a bachelor's degree but no higher degree were $46,931 and $58,762. Which of these numbers is the mean and which is the median? Explain your reasoning.
2.26 Saving for retirement. Retirement seems a long way off and we need money now, so saving for retirement is hard. Once every three years, the Board of Governors of the Federal Reserve System collects data on household assets and liabilities through the Survey of Consumer Finances (SCF). The most recent such survey was conducted in 2007, and the survey results were released to the public in April 2009. The survey presents data on household ownership of, and balances in, retirement savings accounts. Only 53.6% of households own retirement savings accounts. The mean values per household is $148,579, but the median value is just $45,000. For households in which the head of the household is under 35, 42.6% own retirement accounts, the mean is $25,279, and the median $9600. What explains the differences between the two measures of center, both for all households and for the under-35 age group?
2.21 The respitory system can be a limiting factor in maximal exercise performance. Research from the United Kingdom studied the effect of two breathing frequencies on both performance times and several physiological parameters in swimming. Subjects were 10 male collegiate swimmers. Here are their times in seconds to swim 200 meters at 90% of race pace when breathing every second stroke in front-crawl swimming. SWIMTIMES
151.6 165.1 159.2 163.5 174.8
173.2 177.6 174.3 164.1 171.4
Using a calculator or computer, the standard deviation is about
(a) 7.4. (b) 7.8. (c) 8.2.
2.23 The correct units for the standard deviation in Exercise 2.21 are
(a) no units--it's just a number.
(b) seconds.
(c) seconds squared.
2.32 Weight of newborns. The table below gives the distribution of the weight at birth for all babies born in the United States in 2008:
Weight (grams) | Count | Weight (grams) | Count | |
---|---|---|---|---|
Less than 500 | 6,581 | 3,000 to 3,499 | 1,663,512 | |
500 to 999 | 23,292 | 3,500 to 3,999 | 1,120,642 | |
1,000 to 1,499 | 31,900 | 4,000 to 4,499 | 280,270 | |
1,500 to 1,999 | 67,140 | 4,500 to 4,999 | 39,109 | |
2,000 to 2,499 | 218,196 | 5,000 to 5,499 | 4,443 | |
2,500 to 2,999 | 788,148 |
2.50 Older Americans. The attached spreadsheet contains the percentage of Americans in each state who are aged 65 and older. The same data is shown in a stem-and-leaf plot below. OVER65
The decimal point is at the |
7 | 0
8 | 8
9 |
10 | 0139
11 | 378888
12 | 1114456689999
13 | 012222334556688
14 | 0011367
15 | 035
16 | 9
3.26 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?
Mile per gallon. In its Fuel Economy Guide for model year 2010 vehicles, the Enviromental Protection Agency gives data on 1101 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 1082 vehicles is approximately Normal with mean 20.3 miles per gallon (mpg) and standard deviation 4.3 mpg. Use this information in exercises 3.35 and 3.36.
3.35 In my Chevrolet. The 2010 Chevrolet Camaro with an eight-cylinder engine and automatic transmission has a combined gas mileage of 19 mpg. What percent of all vehicles have better gas mileage than the Camaro?
3.36 The bottom 10%. How low must a 2010 vehicle's gas mileage be in order to fall in the bottom 10% of all vehicles?
3.41 Heights of women. The heights of women aged 20 to 29 follow approximately the N(64.3,2.7) distribution. Men the same age have heights distributed as N(69.9,3.1). What percent of young women are taller than the mean height of young men?
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 155.9 pounds and median 144.0 pounds. The first and third quartiles are 124.1 pounds and 173.7 pounds. What can you say about the shape of the weight distribution? Why?