Question

460 Math Activty 7.3 MATH ACTIVITY 7.3 Simulations in Statistics ulatives Purpose: Use spinners to generate random numbers and explore simulation problems. Materials: 1-to-4 and 1-t0-6 Spinners in the Manipulative Kit or Virtual Manipulatives. For the cardstock spinners, bend a paper clip and hold a pencil at the center of the spin- ner, as shown below 1. A certain brand of nonfat yogurt contains one of the letters A, B, C, or D on the inside of the cover. A person collecting one of each type of cover can return them to the store and receive one free container of yogurt. Assuming that each letter has the same chance of being selected, how many yogurts might a person expect to buy on average before getting one of each type of cover? Make a guess. mhhe.com/bbne Rather than buy yogurts, we can devise an experiment (called a simulation) to model the situation. Since there are four types of covers, we can use the 1-to-4 spinner, letting 1, 2, 3, and 4 represent the A, B, C, and D covers, respectively. Spin the 1-to-4 spinner and record the total number of spins needed to get each of the numbers at least once Repeat this experiment 20 times, and record the number of spins needed to get all four numbers for each experiment. 4 2 a. What is the smallest number of your spins needed to get all four numbers? b. What is the greatest number of your spins to get all four numbers? c. What is the average of the numbers of spins to get all four numbers for your 20 experiments? a person might normally be expected to buy before getting all four types of covers. from part c with several other students and compute the average of all of your answers. d. On the basis of your experiments, write a statement about the number of yogurts *e. Results tend to be more accurate for larger numbers of experiments. Pool your data 2. Approximately two out of every five people have type A blood. How many people on average will need to be randomly selected to obtain three people with type A blood? a. Model the situation by using the 1-to-6 spinner 1-to-6 spinner. Cross off one num- ber (for example, the number 6) and designate two of the remain- ing five numbers as representing people with type A blood. Record the total number of spins needed to get three people with type A blood. Type A 2 4 Type A b. Repeat this experiment 20 times, and record the number of spins needed to get three people with type A blood for each experiment. What is the average of the number of spins to get three people with type A blood for your 20 experiments?

Answer 1

(1)

Trial	Number of spins
1	1
2	5
3	27
4	6
5	22
6	7
7	23
8	2
9	21
10	21
11	25
12	3
13	8
14	33
15	5
16	4
17	16
18	8
19	25
20	24

(a) Minimum number of spins =			1
(b) Maximum number of spins =			33
(c) Average number of spins =			14.3
(d) The person might be expected to buy about 14.3 (say 15) yogurts before getting all four types of covers

(e) I have repeated the 20 trials 5 times (this is like comparing your answers with those of four other students)
Student #1 (You)			Student #2			Student #3			Student #4			Student #5
Trial	Number of spins		Trial	Number of spins		Trial	Number of spins		Trial	Number of spins		Trial	Number of spins
1	1		1	30		1	36		1	8		1	29
2	5		2	6		2	15		2	3		2	12
3	27		3	30		3	32		3	10		3	11
4	6		4	11		4	7		4	37		4	19
5	22		5	17		5	16		5	29		5	24
6	7		6	12		6	6		6	32		6	5
7	23		7	18		7	34		7	17		7	33
8	2		8	2		8	36		8	26		8	8
9	21		9	5		9	38		9	15		9	12
10	21		10	40		10	25		10	4		10	31
11	25		11	27		11	15		11	10		11	13
12	3		12	13		12	24		12	11		12	20
13	8		13	27		13	14		13	28		13	8
14	33		14	10		14	10		14	21		14	20
15	5		15	23		15	31		15	17		15	19
16	4		16	34		16	37		16	9		16	16
17	16		17	39		17	39		17	3		17	16
18	8		18	28		18	38		18	11		18	23
19	25		19	9		19	34		19	24		19	4
20	24		20	33		20	28		20	19		20	22

(a) Minimum number of spins =		1			2			6			3			4
(b) Maximum number of spins =		33			40			39			37			33
(c) Average number of spins =		14.3			20.7			25.75			16.7			17.25
(d) Number of yogurts =		15			21			26			17			18

Averages for 5 students:
(a) Minimum number of spins =	3.2
(b) Maximum number of spins =	36.4
(c) Average number of spins =	18.94
(d) Number of yogurts =	19.4