Week 7 - Application Assignment (18 Points)

Part 1) STRUCTURAL INTEGRITY (10 points)

You are a middle school science teacher and you've been working with your students on a special project as part of a unit on structural engineering.You've asked your students to construct a platform at least 1" tall that could hold as much weight as possible before collapsing.But, of course there's a bit of a catch: the only materials that can be used are 5 sheets of notebook paper and a dozen rubber bands to build their platform.On the day the projects are due, you test each platform by placing a 6" x 6" piece of cardboard on top of their construction, and then proceed to add weights to the platform until it collapses.You record the maximum weight each platform could support before collapsing in a data table.Below are the maximum weights (in kilograms) supported by the platforms constructed by the twenty enterprising teams in your seventh and eighth grade science classes.

SEVENTH GRADE TEAMS ( )

4.2

1.6

1.4

0.7

2.8

1.7

2.7

7.4

1.5

2.2

1.8

0.5

1.3

3.1

2.0

2.1

2.3

2.2

1.2

6.8

EIGHTH GRADE TEAMS ( )

3.2

2.2

2.3

2.6

2.1

3.2

1.2

2.8

1.9

1.1

1.8

2.7

1.6

1.6

3.5

1.7

3.3

2.7

2.5

1.8

Additionally, you have entered your science classes into a statewide engineering fair.Each grade is eligible to receive an 'Excellence in Engineering' award if based on each grade's aggregate data (mean and standard deviation) that there is at least a 90% chance that their platforms would hold at least 1 kilogram.Also, any teams able to build a platform that would have been stronger than 99% of last year's entries will be invited to participate in a state-wide engineering day at a local university.Assume that platforms' weights are normally distributed.Last year's entries supported an average of 2.2 kilograms and had a standard deviation of 1.2 kilograms.

1.(2 pts) Calculate descriptive statistics for both the seventh and eighth grade teams (separately).Be sure you include the sample means ( and ) and sample standard deviations ( and ) for both grades.Based on your findings, which grade's platforms supported more weight on average?

We will use descriptive stats in Excel to compare both teams. We can compare the means because we are assuming that the weights are normally distributed. Based on both teams and our histogram the 7^th grade team supported more weights.

(2 pts) Which (if any) of your grades (seventh or eighth) will receive the 'Excellence in Engineering' award?Justify your conclusion by using the normal distribution to calculate the chance that a platform from each grade would be able to hold at least 1 kilogram and by comparing it with the 90% chance.