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?

2.(2 pts) Construct comparative boxplots or histograms for the seventh and eighth grade data sets using Excel. Copy and paste your graph on this assignment document. Discuss the shapes of the individual distributions (normally distributed or not, any outliers, skewness, etc).

3.(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.

4.(2 pts) How is it possible that the grade with the lower average platform weight qualifies for the 'Excellence in Engineering' award but the grade with higher average platform weight does not? (HINT: Use the graphs you have in question two and analyze the shapes of the distributions.)

5.(2 pts) What weight is required for an individual team to qualify for Engineering Day? (Use last year's mean and standard deviation to answer the question and show your work)

Part2) Side Effects for Migraine Medicine(4 points)

In clinical trials and extended studies of a medication whose purpose is to reduce the pain associated with migraine headaches, 2% of the patients in the study experienced weight gain as a side effect. Suppose a random sample of 600 users of this medication is obtained.

1.Explain why you can use normal approximation to binomial distribution to approximate the probabilities below.

2.Approximate, up to 4 decimal digits, the probability that 20 or fewer users will experience weight gain as a side effect.

3.Approximate, up to 4 decimal digits, the probability that 22 or more users experience weight gain as a side effect.

4.Approximate, up to 4 decimal digits, the probability that between 20 and 30 patients, inclusive will experience weight gain as a side effect.

Part 3) Assessing Normality(4 points)

Many statistical procedures require that we draw a sample from a population whose distribution is approximately normal. Often we don't know whether the population is approximately normal when we draw the sample. So the only way we assess whether the population is approximately normal is to examine its sample. Assessing normality is more important for small samples. Below, you'll see some small samples and you'll be asked to assess whether the populations they are drawn from can be treated as approximately normal.

1.The following data set is given. Determine whether it is reasonable to treat the following sample as though it comes from an approximately normal population. Include any charts or graphs you make in Excel here and justify your answer.

2.6

4.2

1.5

2.0

0.6

0.7

6.6

2.2

9.7

1.8

4.2

4.4

0.6

0.2

2.The following normal quantile plot illustrates a sample. Determine whether it is reasonable to treat this sample as though it comes from an approximately normal population. Explain your answer.

3.The following histogram illustrates a sample. Determine whether it is reasonable to treat this sample as though it comes from an approximately normal population. Explain your answer.

4.The following data set is given. Determine whether it is reasonable to treat the following sample as though it comes from an approximately normal population. Include any charts or graphs you make in Excel here and justify your answer.

8.8

11.2

11.6

6.3

9.3

10.5

14.6

8.5

7.3

7.5

5.2

9.0

4.3

9.9

7.8

13.1

12.3

10.1