-Graph, charts, and numbers (data sets, frequency tables, means, medians, percentiles, ranges and standards deviation)

-Probabilities, odds, and expectations (sample spaces and events, The multiplication rule, permutations, and combinations, probabilities and odds, expectations

-The mathematics of normality (Aprox normal data sets, modeling approx normal distributions, normality of random events)

Math 1101

Quiz #3

Name _________________________________________

25 points

You may use a calculator and the notes packet. Show all work to earn full credit.

1. To count whale populations, the “capture” is done by means of a photograph, and the “tagging”

is done by identifying each captured whale through their unique individual pigmentation and

markings. To estimate the population of gray whales in a region of the Pacific between

Northern California and Southern Alaska, 121 gray whales were “captured” and “tagged” in

2007. In 2008, 172 whales were “recaptured.” Of these, 76 had been “tagged” in the 2007

survey. Based on these figures, estimate the population of gray whales in the region. (2 pts)

________________

2. The table shows the ages of the firefighters in the Duluth Fire Department. Find the average

age of the firefighters, rounded to two decimal places. (2 pts)

Age

Frequency

25

2

27

7

28

6

29

9

30

15

31

12

32

9

33

9

37

6

39

4

40

5

43

3

46

3

________________

3. Consider the data set: −𝟒 , 𝟔 , 𝟖 , −𝟓. 𝟐 , 𝟏𝟎. 𝟒 , 𝟏𝟎 , 𝟏𝟐. 𝟔 , −𝟏𝟑 , 𝟓. 𝟏

a. Find the mean/average. (1 pt)

________________

b. Find the five number summary values (listed below) and then make the box plot. (3 pts)

Min = __________ 𝑄1 = __________ Median = ___________ 𝑄3 = ___________ Max = ____________

c. Find the range and interquartile range. (2 pts)

Range = ____________

Interquartile range = ____________

4. Nine people (four men and five women) line up at a checkout stand in a grocery store. (3 pts)

a. In how many ways can they line up?

________________________

b. In how many ways can they line up if the first person must be a woman?

________________________

c. In how many ways can they line up if they must alternate woman, man, woman, man, and

so on?

________________________

5. Bob has 20 different dress shirts. In how many ways can Bob select seven shirts to pack for a

business trip? (2 pts)

________________________

9. Find the probability that a randomly selected student scored

at least a C on their History Class Exam. (1 pt)

_________________

10. A bag contains 12 blue, 10 red, and 8 white marbles. You randomly choose one marble.

a. What are the odds in favor of choosing a red? (1 pt)

________________

b. What are the odds against choosing a blue marble? (1 pt)

________________

11. Consider a normal distribution with first quartile 𝑄1 = 229 and third quartile 𝑄3 = 391. Find

the mean 𝜇 and standard deviation 𝜎. (2 pts)

𝜇 = ___________

𝜎 = ___________

12. A normal distribution has mean 𝜇 = 500 and standard deviation 𝜎 = 35. Approximately what

percent of the data falls between 465 and 605? (2 pts)

________________

13. A fair coin is tossed 3600 times. Let the random variable 𝑌 denote the number of tails tossed.

a. Find the mean 𝜇 and standard deviation 𝜎 of the distribution of the random variable 𝑌. (2 pts)

𝜇 = ___________

𝜎 = ___________

b. Estimate the chances that 𝑌 will fall somewhere between 1800 and 1830. (1 pt)

________________