Download Hint: Divide answer #5a by 50

STANDARD NORMAL CURVE EXPERIMENT
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
13
Frequency
3. Identify the following measurements based on your sample data.
- Enter your sample data into L1 on your calculator
- Answer to the nearest hundredth (2 decimal places)
Mean: _____
Q1: _____
Range: _____
Median: _____
Q3: _____
Mode: _____
Interquartile Range: _____
Standard Deviation: _____
Variance: _____
14
Total
According to the"empirical rule", if you add percentages, you will see that approximately:
• 68% of the distribution lies within one standard deviation of the mean.
• 95% of the distribution lies within two standard deviations of the mean.
• 99% 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. Based on years of research, the expected percentages for the standard normal curve are:
6. Given the empirical rule stated above, does your data approximately follow a normal distribution
pattern? Why or why not?
____________________________________________________________________________________
____________________________________________________________________________________
____________________________________________________________________________________
____________________________________________________________________________________
____________________________________________________________________________________
Sketch a normal curve for each distribution. Label the x-axis values at one, two, and
three standard deviations from the mean.
A. mean = 95; standard deviation = 12
B. mean = 100; standard deviation = 15
C. mean = 60; standard deviation = 6 8.
D. mean = 23.8; standard deviation = 5.2
A set of data has a normal distribution with a mean of 5.1 and a standard deviation
of 0.9. Sketch the normal curve out to 3 standard deviations, and find the percent of
data within each interval.
A. from 4.2 to 5.1
B. from 6.0 to 6.9
C. greater than 6.9
The number of miles on a car when a certain part fails is normally distributed, with
a mean of 60,000 and a standard deviation of 5000.
A. Sketch the normal curve for the distribution. Label the x-axis values at one, two, and
three standard deviations from the mean.
B. What is the probability that the part will NOT fail between 55,000 and 65,000 miles?
A normal distribution has a mean of 50 and a standard deviation of 6. Sketch the
normal curve, and find the probability that a value selected at random is in the
given interval.
A. from 44 to 50
B. from 38 to 56
C. from 50 to 62
D. at least 50
E. at most 56
F. at least 38