Intro to Survey Mathematics

I need a graphing assignment completed by Friday. You will need to incorporate information from an original assignment I did to complete this one. I will include the original assignment also feedback from the teacher for that assignment and the graphing assignment. 

Name: weeks 9-11

Graphing Island

Directions

Your population is thriving on your island. The data you have collected now needs to be displayed and further analyzed. Use the charts you created in the probability portion in weeks 1-3 for this part of the project. Always show your calculations or explain how you used technology. Take a picture of your calculator if you used that or submit your excel worksheet.

1. a. Create a Scatter Plot using the total population for each of the years from the Probability Island. The horizontal axis should always represent time.

b. Use linear regression or a trendline in Excel to find the equation of the best fit line.

c. Find the Correlation Coefficient. Explain what this means for your data.

d. Use the equation to predict the population in year 20.

2. a. Use the first and last data points of the total population for each of the years from the Probability Island to find a linear equation to model the data.

b. Graph the equation.

c. Compare the slope of the Linear Regression Line of question 1 with the slope of this line. Provide an explanation of why they may similar or differ.

d. Use the equation to predict the population in year 20.

3. a. Assume that (0,150) represents the vertex of a quadratic equation. Find a quadratic equation using the tenth-year population as another point.

b. Graph the equation.

c. Use the equation to predict the population in year 20.

4. Using the equation y = 2×2 -9x +4, explain and demonstrate how to find the x-intercepts, the y-intercept, the axis of symmetry, and the vertex of a quadratic equation.

Name: weeks

1

–

3

Probability Island

You will collect the data for the population of an island community. Then you will use and evaluate probability models. You will be using this data for the next parts of your project.

Your ship is carrying

1

5

0

passengers –

7

5

adult females and

75

adult males – all in good health. An intense storm occurs and your ship hits rocks and wrecks off the coast of a deserted island in the Pacific

O

cean. This island has the necessary natural resources for human survival.

The ages of your passengers are recorded in the table below.

10

10

10

10

10

15

15

15

15

15

75

Age		Female		Male
2 0-2 9								10
30-39
4 0-49
50-59							15
6 0-69
70+
	Total				75

Directions: Probability of births

1. For each woman aged

20

-39, roll a die one time. If you get a 6, the woman has a baby. Flip a coin. If it’s heads, it’s a girl. If it’s tails, it’s a boy. Complete Chart 1 on the next page to track the births per year and the number of boys and girls. Repeat this simulation for ten years. Note: There are 20 women in these age groups. They are numbered 1 through 20 in the chart. For the purposes of this project, assume all women in these age groups remain capable of having children; keep everyone in their assigned age groups.

2. Assuming the births occur as recorded, and that no one dies, what is the population of your island at the end of the ten-year period? Use

Chart 2

to clearly show the population of your island at the end of each year.

3. Showing your work, calculate the theoretical probability and the experimental probability of:

a) A woman giving birth in any given year

b) Having a baby and it being a girl

c) Having a baby and it being a boy

4. Compare the theoretical probabilities to the experimental probabilities. Use these results to discuss any similarities and/or differences.

Chart 1.

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Woman	Year 1	Year 2	Year 3	Year 4	Year 5	Year		6	Year		7	Year		8	Year		9		Year
					1																																																																																																																																																																								X																G
							2																B
				3
								4
			5
11
12
13
14
16
17
18
19
20
Total boys	O								0
Total girls
Total Births

Chart 2

Year

0

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3

4

5

6

7

8

9

10

Male

75

76

86

91

Female

75

79

81

82

88

89

89

91

91

Total

182

	76		79		81		82		86			89				91
84		88
150	155	157	161	165	170	174	175	178		182

3a- The probability of a woman having a baby any given year would be.

The probability would be ½. You have a total of 10 years and 20 women. So in 10 years its possible 20 women can give birth any given year.

3b- The probability of a woman having a baby and it being a girl would.

A total of 16 girls were born over the 10 years out of 20 women. That would be a total out of 4/5.

3c-The probability of a woman having a baby and it being a boy would be.

A total of 16 boys were born over the 10 years out of 20 women. That would also be a total of 4/5.

4. Out of 20 women in 10 years it is possible for any of them to get pregnant. 16 girls are born and 16 boys are born which is pretty even and would be the same just different genders.