Transcript Empirical Rule & Standard Normal Distributions

A young athlete runs the 400 meter dash and
records his trials in seconds. Find the mean and
standard deviation for the data from his sprints:
50.6, 50.9, 49.1, 51.3, 50.5,
49.7, 51.5, 49.8, 51.1, 48.9,
50.3, 49.2, 51.2, 50.4, 52.8.
Today you will be able to:
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Calculate the mean
Calculate the mode
Calculate the median
Calculate the range, and IQR
Calculate the variance
Calculate the standard deviation
Do a statistical analysis and compare data sets
Use your calculator to run an analysis
Identify measures of center
Identify measure of variability
Label the percentage intervals of a normal distribution
Determine probability using empirical rule 68-95-99.7
Determine probability using z-scores
Standard Normal Distributions
April 6, 2016
Empirical Rule
Main Entry:
em·pir·i·cal
Function:
adjective
Date:
1569
1 : originating in or based on observation or experience
<empirical data> 2 : relying on experience or observation
alone often without due regard for system and theory <an
empirical basis for the theory> 3 : capable of being verified
or disproved by observation or experiment <empirical laws>
about 68% of a data set lies in the range
X   to X  
about 95% of a data set lies in the range
X  2 to X  2
X  3 to X  3
almost all of a data set lies in the range
34% of your data
34% of your data
13.5% of your data
2.35% of your data
13.5% of your data
2.35% of your data
0.15% of your data
0.15% of your data
x
Normal Distribution:
A bell-shaped, normal curve that is symmetric
about the mean; total area under the curve is 1
34% of your data
34% of your data
13.5% of your data
2.35% of your data
13.5% of your data
2.35% of your data
0.15% of your data
0.15% of your data
x
Standard Normal Distribution
A normal distribution has a mean and a standard deviation. Find the indicated
probability for a randomly selected x-value from the distribution.
1.)
3.)
P( X  x  X  2 )
P( x  X   )
2.)
P( x  X   )
4.)
P( X  x  X   )
Give the percent of the area under the normal curve
represented by the shaded region.
x
Standard Normal Distribution
Your Turn…
A normal distribution has a mean of 27 and a
standard deviation of 5.
• a.) Find the probability that a randomly selected
value will be between 22 and 32.
• b.) Find the probability that a randomly selected
value will be between 12 and 27.
• c.) Find the probability that a randomly selected
value will be between 17 and 37.
• d.) Find the probability that a randomly selected
value will be at least 22.
A young athlete runs the 800 meter dash and
records his trials in seconds. Find the mean and
standard deviation for the data from his sprints:
50.6, 50.9, 49.1, 51.3, 50.5, 49.7, 51.5, 49.8,
51.1, 48.9, 50.3, 49.2, 51.2, 50.4, 52.8.
Interval
X   to X  
Numerical
Interval
Fraction of data in
interval
Empirical
Rule
68%
X  2 to X  2
95%
X  3 to X  3
99.7%
z
X X

Normal Score of x
Today you will be able to:













Calculate the mean
Calculate the mode
Calculate the median
Calculate the range, and IQR
Calculate the variance
Calculate the standard deviation
Do a statistical analysis and compare data sets
Use your calculator to run an analysis
Identify measures of center
Identify measure of variability
Label the percentage intervals of a normal distribution
Determine probability using empirical rule 68-95-99.7
Determine probability using z-scores