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Flashcards in Part 4: Data Analysis Deck (42)
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31

Exercise 8. How many 3-digit positive integers are odd and do not contain the digit 5 ?

8 * 9 * 4 = 288

32

Exercise 9. From a box of 10 lightbulbs, you are to remove 4. How many different sets of 4 lightbulbs could you remove?

1 (gah!)
10!/4!(10 - 4!) = 10 * 9 * 8 * 7 / 24 = 210

33

Exercise 10. A talent contest has 8 contestants. Judges must award prizes for first, second, and third places, with no ties.
(a) In how many different ways can the judges award the 3 prizes?
(b) How many different groups of 3 people can get prizes?

8 * 7 * 6 = 336

336/6 = 56


34

Exercise 11. If an integer is randomly selected from all positive 2-digit integers, what is the probability that the integer chosen has
(a) a 4 in the tens place?
(b) at least one 4 in the tens place or the units place? (c) no 4 in either place?

a) 1/9
b) P(AorB) = 10/90 + 9/90 = 18/90 = 1/5
c) 4/5

35

Exercise 12. In a box of 10 electrical parts, 2 are defective.
(a) If you choose one part at random from the box, what is the probability that it is not
defective?
(b) If you choose two parts at random from the box, without replacement, what is the probability that both are defective?

a) 4/5

b) 1/5 * 1/9 = 1/45

36

Exercise 13. A certain college has 8,978 full-time students, some of whom live on campus and some of whom live off campus.
The following table shows the distribution of the 8,978 full-time students, by class and living arrangement.


Freshmen
Sophomores

Juniors

Seniors

Live on campus
1,812
1,236
950
542
Live off campus

625


908
1,282

1,623

(a) If one full-time student is selected at random, what is the probability that the student who is chosen will not be a freshman?
(b) If one full-time student who lives off campus is selected at random, what is the probability that the student will be a senior?
(c) If one full-time student who is a freshman or sophomore is selected at random, what is the probability that the student will be a student who lives on campus?

a) 8978 -1812 - 625)/ 8978 = 73%

b) 1623/ 1623 + 1282 + 908 + 625 = 36.6%

c) 1812 + 1236 / 1812 + 1236 + 625 + 908 = 66.5%

37

Exercise 14. Let A, B, C, and D be events for which P(AorB)=0.6, P(A)=0.2, P(CorD)=0.6, and P(C)=0.5.
The events A and B are mutually exclusive, and the events C and D are independent.
(a) Find P(B).
(b) Find P(D).

P(B) = 0.4
0.2 = P(D)

38

Exercise 15. Lin and Mark each attempt independently to decode a message. If the probability that Lin will decode the message is 0.80 and the probability that Mark will decode the message is 0.70, find the probability that
(a) both will decode the message
(b) at least one of them will decode the message
(c) neither of them will decode the message

a) .8 * .7 = 0.56
b) .8 + .7 - .56 = 1.50 - .56 = 0.94
c) 0.2 * 0.3 = 0.06

39

Exercise 16. Data Analysis Figure 21 below shows the graph of a normal distribution with mean m and standard deviation d, including approximate percents of the distribution corresponding to the six regions shown.
Data Analysis Figure 21
Suppose the heights of a population of 3,000 adult penguins are approximately normally distributed with a mean of 65 centimeters and a standard deviation of 5 centimeters.
(a) Approximately how many of the adult penguins are between 65 centimeters and 75 centimeters tall?
(b) If an adult penguin is chosen at random from the population, approximately what is the probability that the penguin’s height will be less than 60 centimeters? Give your answer to the nearest 0.05.

a) 3000 * 0.48 = 1440

b) 16%

40

Exercise 17. This exercise is based on the following graph.
Data Analysis Figure 22
(a) For which year did total expenditures increase the most from the year before?
(b) For 2001, private school expenditures were what percent of total expenditures? Give your answer to the nearest percent.

a) 1998
b) 30/160 = 19%

41

Exercise 18. This exercise is based on the following data.
Data Analysis Figure 23
(a) In 2001, how many categories each comprised more than 25 million workers?
(b) What is the ratio of the number of workers in the Agricultural category in 2001 to the projected number of such workers in 2025 ?
(c) From 2001 to 2025, there is a projected increase in the number of workers in which of the following three categories?
Category1: Sales
Category2: Service
Category3: Clerical

a) agriculture, manufacturing, clerical

b) 150mil * .18 : 175 mil * .24 = 27 mil : 42 mil = 9: 14

c) Service , Sales, Clerical (All)


42

Exercise 19. This exercise is based on the following data.
Data Analysis Figure 24
(a) In 2003 the family used a total of 49 percent of its gross annual income for two of the categories listed. What was the total amount of the family’s income used for those same categories in 2004 ?
(b) Of the seven categories listed, which category of expenditure had the greatest percent increase from 2003 to 2004 ?

a) real estate and savings

b) Miscellaneous