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...

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

1. = __________


2. 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.