1. A data set with whole numbers has a low value of 20 and a high value of 82. Find the class width for a frequency table with seven classes. Find the class limits for a frequency table with seven classes.

	Lower class limit Upper class limit
First class
Second class
Third class
Fourth class
Fifth class
Sixth class
Seventh class

2. The ogives shown are based on U.S. Census data and show the average annual personal income per capita for each of the50 states.The data are rounded to the nearest thousand dollars.

(i) Ogive

(ii) Ogive Showing Cumulative Percentage of Data

(a) How were the percentages shown in graph (ii) computed? The percentages in graph (ii) were computed by dividing each of the cumulative frequencies ingraph (i)by 100 and then converting those values into decimals.The percentages in graph (ii) were computed by dividing each of the cumulative frequencies ingraph (i)by 50 and then converting those values into percents. The percentages in graph (ii) were computed by multiplying each of the cumulative frequencies ingraph (i)by 100 and then converting those values into decimals.The percentages in graph (ii) were computed by multiplying each of the cumulative frequencies ingraph (i)by 50 and then converting those values into percents.The percentages in graph (ii) were computed by dividing each of the cumulative frequencies ingraph (i)by 50 and then converting those values into fractions. (b) How many states have average per capita income less than 37.5 thousand dollars? (c) How many states have average per capita income between 42.5 and 52.5 thousand dollars? (d) What percentage of the states have average per capita income more than 47.5 thousand dollars? %

3. How long does it take to finish the 1161-mile Iditarod Dog Sled Race from Anchorage to Nome, Alaska? Finish times (to the nearest hour) for 57 dogsled teams are shown below.

261	271	236	244	279	296	284	299	288
288	247	256	338	360	341	333	261	266
287	296	313	311	307	307	299	303	277
283	304	305	288	290	288	289	297	299
332	330	309	328	307	328	285	291	295
298	306	315	310	318	318	320	333	321
323	324	327

For this problem, use five classes.(a) Find the class width. (b) Make a frequency table showing class limits, class boundaries, midpoints, frequencies, relative frequencies, and cumulative frequencies. (Round your relative frequencies to two decimal places.)

Class Limits	Class Boundaries	Midpoint	Frequency	Relative Frequency	Cumulative Frequency

b. draw a graph

4. The following data represent glucose blood levels (mg/100 ml) after a 12-hour fast for a random sample of 70 women (Reference:American Journal of Clinical Nutrition, Vol. 19, pp. 345-351).

45	66	83	71	76	64	59	59	76	82
80	81	85	77	82	90	87	72	79	69
83	71	87	69	81	76	96	83	67	94
101	94	89	94	73	99	93	85	83	80
78	80	85	83	84	74	81	70	65	89
70	80	84	77	65	46	80	70	75	45
101	71	109	73	73	80	72	81	63	74

For this problem, use six classes.(a) Find the class width. (b) Make a frequency table showing class limits, class boundaries, midpoints, frequencies, relative frequencies, and cumulative frequencies. (Round your relative frequencies to four decimal places.)

Class Limits	Class Boundaries	Midpoint	Frequency	Relative Frequency	Cumulative Frequency

draw a graph

5. In archaeology, the depth (below surface grade) at which artifacts are found is very important. Greater depths sometimes indicate older artifacts, perhaps from a different archaeological period. The figure below is aback-to-back stem plotshowing the depths of artifact locations at two different archaeological sites. These sites are from similar geographic locations. Notice that the stems are in the center of the diagram. The leaves forSite Iartifact depths are shown to the left of the stem, while the leaves forSite IIare to the right of the stem.(a) What are the least and greatest depths of artifact finds at Site I?

Least	cm
Greatest	cm

What are the least and greatest depths of artifact finds at Site II?

Least	cm
Greatest	cm

6. How long did real cowboys live? One answer may be found in the book The Last Cowboys by Connie Brooks (University of New Mexico Press). This delightful book presents a thoughtful sociological study of cowboys in West Texas and Southeastern New Mexico around the year 1890. A sample of 32 cowboys gave the following years of longevity:

58	52	68	86	72	66	97	89	84	91	91
92	66	68	87	86	73	61	70	75	72	73
85	84	90	57	77	76	84	93	58	47

(a) Make a stem-and-leaf display for these data. (Use the tens digit as the stem and the ones digit as the leaf. Enter numbers from smallest to largest separated by spaces. Enter NONE for stems with no values.)

Longevity of Cowboys

7. Wetlands offer a diversity of benefits. They provide a habitat for wildlife, spawning grounds for U.S. commercial fish, and renewable timber resources. In the last 200 years, the United States has lost more than half its wetlands. Environmental Almanac gives the percentage of wetlands lost in each state in the last 200 years. For the 30 of the lower 48 states, the percentage loss of wetlands per state is as follows.

45	35	50	51	27	59
48	59	50	60	38	38
42	68	83	37	33	71
35	42	27	35	45	87
50	55	87	24	90	9

Make a stem-and-leaf display of these data. (Use the tens digit as the stem and the ones digit as the leaf. Enter NONE in any unused answer blanks.)

Percent of Wetlands Lost

How are the percentages distributed? Is the distribution skewed? Are there any gaps? (Select all that apply.) The percentages are concentrated from 20% to 60%.There is a gap showing that none of the lower 48 states has lost from 60% to 69% of its wetlands.There are no gaps in the data.These data are fairly symmetric, perhaps slightly skewed right.These data are strongly skewed left.There is a gap showing that none of the lower 48 states has lost from 10% to 19% of its wetlands.The percentages are concentrated from 60% to 90%.

8. Does it pay to ask for a raise? A national survey of heads of households showed the percentage of those who asked for a raise and the percentage who got one. According to the survey, of the women interviewed, 28% had asked for a raise, and of those women who had asked for a raise, 45% received the raise. If a woman is selected at random from the survey population of women, find the following probabilities. (Enter your answers to three decimal places.)(a) P(woman asked for a raise) (b) P(woman received raise, given she asked for one) (c) P(woman asked for raise and received raise)

9. Allergic reactions to poison ivy can be miserable. Plant oils cause the reaction. Researchers at Allergy Institute did a study to determine the effects of washing the oil off within 5 minutes of exposure. A random sample of 1000 people with known allergies to poison ivy participated in the study. Oil from the poison ivy plant was rubbed on a patch of skin. For 500 of the subjects, it was washed off within 5 minutes. For the other 500 subjects, the oil was washed off after 5 minutes. The results are summarized in the following table.

Reaction	Within 5 Minutes	After 5 Minutes	Row Total
None Mild Strong	393 55 52	59 341 100	452 396 152
Column Total	500	500	1000

Let's use the following notation for the various events: W = washing oil off within 5 minutes, A = washing oil off after 5 minutes, N = no reaction, M = mild reaction, S = strong reaction. Find the following probabilities for a person selected at random from this sample of 1000 subjects. (Use 3 decimal places.)

(a)	P(N)
	P(M)
	P(S)

(b)	P(N | W)
	P(S | W)

(c)	P(N | A)
	P(S | A)

(d)	P(N and W)
	P(M and W)

(e) P(N or M).

9. There is money to send four of nine city council members to a conference in Honolulu. All want to go, so they decide to choose the members to go to the conference by a random process. How many different combinations of four council members can be selected from the nine who want to go to the conference?

10. Compute the following.(a) P_{6, 2}. (b) C_{6, 2}. (c) P_{12, 12}. (d) C_{13, 13}.