Title: Understandable Statistics Eighth Edition By Brase and Brase Prepared by: Lynn Smith Gloucester Count
1Understandable StatisticsEighth EditionBy Brase
and BrasePrepared by Lynn SmithGloucester
County College
- Section 6.1
- Graphs of Normal Probability Distributions
2The Normal Distribution
3Properties of The Normal Distribution
?
The curve is bell-shaped with the highest point
over the mean, ?.
4Properties of The Normal Distribution
?
The curve is symmetrical about a vertical line
through ?.
5Properties of The Normal Distribution
?
The curve approaches the horizontal axis but
never touches or crosses it.
6Properties of The Normal Distribution
? ? ?? ? ? ?
The transition points between cupping upward and
downward occur above ? ? and ? ? .
7The Normal Density Function
- This formula generates the density curve which
gives the shape of the normal distribution.
8 The Empirical Rule
Approximately 68 of the data values lie is
within one standard deviation of the mean.
68
One standard deviation from the mean.
9The Empirical Rule
Approximately 95 of the data values lie within
two standard deviations of the mean.
95
Two standard deviations from the mean.
10The Empirical Rule
Almost all (approximately 99.7) of the data
values will be within three standard deviations
of the mean.
99.7
Three standard deviations from the mean.
11Application of the Empirical Rule
- The life of a particular type of light bulb is
normally distributed with a mean of 1100 hours
and a standard deviation of 100 hours. - What is the probability that a light bulb of this
type will last between 1000 and 1200 hours? - Approximately 68
12Control Chart
- a statistical tool to track data over a period of
equally spaced time intervals or in some
sequential order
13Statistical Control
- A random variable is in statistical control if it
can be described by the same probability
distribution when it is observed at successive
points in time.
14To Construct a Control Chart
- Draw a center horizontal line at ?.
- Draw dashed lines (control limits) at
- ? ? ? ? and ? ? ??.
- The values of ?? and ? may be target values or
may be computed from past data when the process
was in control. - Plot the variable being measured using time on
the horizontal axis.
15Control Chart
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16Control Chart
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17Out-Of-Control Warning Signals
- I One point beyond the 3? level
- II A run of nine consecutive points on one
side of the center line at target ? - III At least two of three consecutive points
beyond the 2? level on the same side of the
center line.
18Probability of a False Alarm
19Is the Process in Control?
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20Is the Process in Control?
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13
21Is the Process in Control?
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