Chapter 6: The Normal Distribution Pinkie LabStudent Learning Outcomes: The student will compare...

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Chapter 6: The Normal Distribution Pinkie Lab Student Learning Outcomes: The student will compare empirical data and a theoretical distribution to determine if everyday experiment fits a continuous...

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Chapter 6: The Normal Distribution Pinkie Lab
Student Learning Outcomes: The student will compare empirical data and a theoretical distribution to determine if everyday experiment fits a continuous distribution.
I. Collect the Data
1. The lengths of the pinkie finger of 30 adults are given below, to the nearest 0.5 cm.

5	5	5	5.5	5.5
5.5	5.5	5.5	5.5	5.5
6	6	6	6	6
6	6	6	6	6
6	6	6	6.5	6.5
6.5	6.5	6.5	7	7

2. Construct a histogram. Make 5 – 8 intervals. Sketch the graph using a ruler and pencil. Scale the axes. Staple your histogram to this lab. REMEMBER: NO endpoint of an interval is a data value.
3. Calculate the following

= __________
s = __________

4. Draw a smooth curve through the top of the bars of the histogram. Use 1 - 2 complete sentences to describe the general shape of the curve. (Keep it simple. Does the graph go straight across, does it have a V shape, does it have a hump in the middle or at either end, etc.?)
II. Analyze the Data
Using your sample mean, sample standard deviation, and histogram to help, what was the approximate theoretical distribution of the data?

X ____________
How does the histogram help you arrive at the approximate distribution? (Use 1-2 complete sentences.)

III. Describe the Data
Using the data in Part I:
Remember: IQR = Q3 – Q1

The IQR goes from ________ to _________.
IQR = ______.
The 15^th percentile is _____________.
The 85^th percentile is ______________.
The median is ___________.
The empirical probability that a randomly chosen pinkie length is less than 5.5 cm = _____________.
Explain the meaning of the 85^th percentile of this data.

IV. Theoretical Distribution
Using the theoretical distribution in Part II:

The IQR goes from _____________ to ______________.
IQR = ___________.
The 15^th percentile is _____________.
The 85^th percentile is ______________.
The median is ___________.
The theoretical probability that a randomly chosen pinkie length is less than 5.5 cm = _____________.
Explain the meaning of the 85^th percentile of this distribution.

V. Discussion Question

Do the data from “Collect the Data” give a close approximation to the theoretical distribution in “Analyze the Data?” In complete sentences and comparing the result in “Describe the Data” and “Theoretical Distribution”, explain why or why not.

005_cayapo-cmiufnee.doc

Answered Same Day Dec 22, 2021

Robert · Accepted Answer

1) 2. 
1) 
  A histogram has been constructed with 5 bins.  
    3.   93.5x , 52.0s  
    4.   A smooth curve has been drawn on top of the bars of the histogram in the same figure. 
The graph has an inverted V shape with two little humps on the right side of the graph.
2) We can say that Approximately X~ N(5.93, 0.52). From the Histogram we can see that the 
curve is almost normal but for a little hump on one side of the graph. If sample size will be 
increased it will approximately be Normal. From the sample, we get the mean and standard 
deviation.  
3) To calculate the quartiles and percentiles , we make the following table: 
 length 
Frequency Percentage Cumulative 
percentage 
5 3 10 10 
5.5 7 23.3333333 33.

Chapter 6: The Normal Distribution Pinkie Lab Student Learning Outcomes: The student will compare empirical data and a theoretical distribution to determine if everyday experiment fits a continuous...

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