Download Complete the following questions on edmodo.

AP Statistics
Mrs. LaPlaca
Chapter 9
Chapter 9: Sampling Distributions
Young Women’s Heights
In this activity you will use the graphing calculator to sample from this
distribution and then use Post –it Notes to construct a distribution of averages.
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The height of young women varies approximately according to the normal
distribution, N(64.5, 2.5).
The population of young women is normally distributed with mean
m = 64.5inches and standard deviation s = 2.5 inches.
The random variable measured is X = height of a randomly selected
young woman.
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If we choose one woman at random, the heights we get in repeated
choices follow the N(64.5, 2.5) distribution. On your calculator, clear L1.
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Simulate the heights of 100 randomly selected young women and store
these heights in L1.
 Place your cursor at the top of L1, on the name (not below it)
 Press MATH, choose PRB, choose “randNorm(“
 Type: randNorm( m , s , n) => randNorm(64.5, 2.5, 100)
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Plot a histogram of the 100 heights as follows.
 Clear all functions in the “Y =” window and turn off all STAT PLOTS.
 Set WINDOW dimensions to X[57, 72] with a scale of 2.5 and Y[-10, 45]
with a scale of 5.
o This extends 3 standard deviations to either side of the mean,
64.5.
 Define PLOT 1 to be a histogram using the heights in L1.
 Press GRAPH to plot the histogram.
Complete the following questions on edmodo.
1. Describe the approximate shape of your histogram. Use clear, appropriate
statistical vocabulary. (See Chapter 1 if necessary)
2. Approximately how many heights should there be within 3s of the mean?
3. Use TRACE to count the actual number of heights in your data within 3s .
How many heights do you have in 3s ?
4. How many heights should there be within 2s of the mean?
5. Use TRACE to count the actual number of heights in your data within 2s
How many heights do you have in 2s ?
6. How many heights should there be within 1s of the mean?
7. Use TRACE to count the actual number of heights in your data within 1s
How many heights do you have in 1s ?
8. Compare your results in #3 through #7. Compare the numbers you
would expect to get and the ones you actually have in your data. Are they
exact or fairly close?
9. Use 1 – Vars Stat to find the mean, median, and standard deviation for
your data. Record your results.
10. Compare your X with the population mean m = 64.5. Compare the
sample standard deviation s with s = 2.5. How do the mean and median
for your 100 heights compare?
11. What does the mean/median comparison tell you about the shape of your
distribution?
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Define PLOT 2 to be a boxplot using L1 and then GRAPH again.
 The boxplot will be plotted above the histogram.
12. Does the boxplot appear roughly symmetric?
13. How close is the median in the boxplot to the mean of the histogram?
14. Based on the appearance of the histogram and the boxplot, and a
comparison of the mean and median, would you say that the distribution
is nonsymmetric, moderately symmetric, or very symmetric?
15. Bring up your calculator to me to check your data and graphs.
Repetition
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Run: randNorm( m , s , n) again (four more times).
For each simulation
o Determine the shape of the distribution.
o Find numeric calculations
o Apply the Emperical Rule to your data set.
o Compare the mean/median to determine shape.
o Essentially, repeat steps #1 through 14 four more times. THIS is
formal data analysis.
o DO NOT answer them formally on edmodo for these FOUR
simulations
From each time, you will only record the mean X , median, and standard
deviation s for each simulation.
These answers will be #16, #17, #18, and #19.
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You will need the mean X for each sample for an activity tomorrow.