Understandable Statistics Eighth Edition By Brase and Brase Prepared by: Lynn Smith Gloucester Count

1
Understandable StatisticsEighth EditionBy Brase
and BrasePrepared by Lynn SmithGloucester
County College

• Section 6.1
• Graphs of Normal Probability Distributions

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The Normal Distribution
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Properties of The Normal Distribution
?
The curve is bell-shaped with the highest point
over the mean, ?.
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Properties of The Normal Distribution
?
The curve is symmetrical about a vertical line
through ?.
5
Properties of The Normal Distribution
?
The curve approaches the horizontal axis but
never touches or crosses it.
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Properties of The Normal Distribution
? ? ?? ? ? ?
The transition points between cupping upward and
downward occur above ? ? and ? ? .
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The Normal Density Function

• This formula generates the density curve which
  gives the shape of the normal distribution.

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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.
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The Empirical Rule
Approximately 95 of the data values lie within
two standard deviations of the mean.
95
Two standard deviations from the mean.
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The 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.
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Application 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

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Control Chart

• a statistical tool to track data over a period of
  equally spaced time intervals or in some
  sequential order

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Statistical 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.

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To 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.

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Control Chart
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Control Chart
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Out-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.

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Probability of a False Alarm
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Is the Process in Control?
???? ???? ? ???? ????
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Is the Process in Control?
???? ???? ? ???? ????
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Is the Process in Control?
???? ???? ? ???? ????
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