Transcript Chapter 16 PPT

Discrete Math
16.1
• Approximate Normal
• Approximately Normal Distribution: Almost a
bell shape curve.
• Normal Distribution: Bell shape curve. All
perfect bell shape curves are normal curves.
Discrete Math
16.2
• Normal Distribution:
center = median (M) = mean ()
• Approx Normal: Median  Mean.
• Point of inflection: transition point of
being bent upward to downward.
• Normal Distribution: The standard
Deviation equals the distance between a
point of inflection and the axis of
symmetry.
To be continued…
Discrete Math
16.2 (Continued...)
• Q1   - (0.675)
• Q3   + (0.675)
Discrete Math
16.3 Standardizing Normal Data
Measuring data values using the standard deviation.
• Standardizing
• Original Data x
(z-value)
Standardized Data z = (x-) / 
Discrete Math
16.4
• 68 - 95 - 99.7 Rule
• 68% of data within one standard deviation
from the mean.
• 95% of data within two standard deviations
from the mean.
• 99.7% of data within three standard
deviations from the mean.
• Range  6
Discrete Math
16.5 - 7
• Honest coin principal: A coin is tossed n
times and X is the number of heads. The
random variable X has an approximately
normal distribution with mean  = n / 2
and standard deviation  = n / 2
• 256 tosses:  = 256 / 2 = 128,  =  256 / 2 = 8
To be continued…
Discrete Math
16.5 - 7 (Continued...)
• Dishonest coin principal: A dishonest
coin is tossed n times and X is the
number of heads. Suppose p is the
probability of heads and (1-p) is the
probability of tails. The random variable
of X has an approximately normal
distribution with mean  = n * p and
standard deviation  = ( n * p * (1 - p))
• 1000 light bulbs, 20% defects:  = 1000(.20) =
200
 =  1000 * (.20) * (1 - .20)
To be continued…
Discrete Math
16.5 - 7 (Continued...)
• Standard Error: The standard deviation
of the sampling distribution expressed
as a percentage.
•/N
• Confidence Intervals: 95% two standard
deviations from the mean.
• 99.7 three standard deviations from the mean.
Discrete Math