Download AFM Sleep Statistics - Empirical Rule Activity

Score
Name:_______________________________
AFM
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The US National Sleep Foundation suggests seven to nine hours of sleep a night for adults. The Foundation conducted a survey
in 2002 that suggest as many as 75% of Americans had problem sleeping, with one-third being so sleepy that it affected their
daily lives. While sleep undergoes a wide variety of modifications during the human life span, all aspects have a relatively
normal distribution pattern.
You will be performing your own statistical study on sleep, analyzing the distribution of a sample set of data.
1. Using your TI-84+ calculator, collecting a set of data using the random number generator function.
- Press MATH, move over to PRB, select #5 randInt(
- Type in randInt( 1 , 14 , 50 ) STO→ L1
OR
randInt( 1 , 12 , 50 ) STO  2nd 1
- This will randomly select 50 numbers between 1 and 14, inclusively and place them in List 1
- Record these numbers below from LIST 1, as numbers of hours slept each day.
- These numbers, which represent a survey of 50 people’s sleep hours, will be your sample data set.
Sleep hours:
2. Complete the frequency chart below based on your sample data
Hours
Slept
1
2
3
4
5
6
7
8
9
10
11
12
Frequ
ency
3. Identify the following measurements based on your sample data.
- Enter your sample data into a list on your calculator
- You may use a single list OR double list
- Answer to the nearest tenth
Mean: _____
Q1: _____
Range: _____
Median: _____
Q3: _____
Mode: _____
Interquartile Range: _____
Standard Deviation: _____
Variance: _____
Total
According to the"empirical rule", if you add percentages, you will see that approximately:
• 68.1% of the distribution lies within one standard deviation of the mean.
• 95.4% of the distribution lies within two standard deviations of the mean.
• 99.8% of the distribution lies within three standard deviations of the mean.
4. Using the normal distribution bell curve below and your data results, identify the
x  _____
following:
x    _____
x    _____
x  2  _____
x  3  _____
x  2  _____
x  3  _____
5. Using the 50 numbers from your sample data, answer the following:
a. How many of your data numbers lie within the range of ONE standard deviation? _______
b. What percent your data numbers lie within the range of ONE standard deviation? _______%
Hint: Divide answer #5a by 50
c. How many of your data numbers lie within the range of TWO standard deviations? _______
d. What percent your data numbers lie within the range of TWO standard deviations? _______%
Hint: Divide answer #5c by 50
e. How many of your data numbers lie within the range of THREE standard deviations? _______
f. What percent your data numbers lie within the range of THREE standard deviations? _______%
Hint: Divide answer #5e by 50
6. Given the empirical rule stated above, does your data approximately follow a normal distribution
pattern? Why or why not?
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