ooN – population sizeon – Total sample sizeoXi – Number of items in the population with outcome ioxi – Number of items in the sample with outcome i°Hypergeometric Distribution ExampleExample: 3 light bulbs were selected from 10. Of the 10 there were 4 defective. What is the probability that 2 of the 3 selected are defective?

Chapter 6: Introduction to Continuous Probability
Distributions
10/25/2015
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6.1 The Normal Probability Distribution
Is a bell-shaped distribution with the following properties:
o
1. It is unimodal; that is, the normal distribution peaks at a
single value
o
2. It is symmetrical; this means that the two areas under the
curve between the mean and any two points equidistant on
either side of the mean are identical
o
3. The mean, median, and mode are equal
o
4. The normal approaches the horizontal axis on either side of
the mean toward plus and minus infinity. In more formal
terms, the normal distribution is asymptotic to the x axis.
o
5. The amount of variation in the random variable determines
the height and spread of the normal distribution
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Normal Probability Density Function
x – any value of the continuous random variable
o – population standard deviation
Pie – 3.14159
e – Base of the natural log = 2.71828…
u – population mean
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Finding Normal Probabilities
Because x is a continuous random variable, the probability, P(x), is
equal to 0 for any particular x
The probability for an range of values between x1 and x2 is defined
by the area under the curve between these two values.
P(a < x < b)
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The standard normal distribution
A normal distribution that has a mean = 0.0 and a standard
deviation = 1.0
The horizontal axis is scaled in z-values that measure the number of
standard deviations a point is from the mean
Values above the mean have positive z-values
Values below the mean have negative z-values

z – scaled value (the number of standard deviations a point x is from
the mean)
x – any point on the horizontal axis
u – mean of the specific normal distribution
o – standard deviation of the specific normal distribution
Any normal distribution (with any mean and standard deviation
combination) can be scaled into the standard normal distribution (z)
Any specific value, x, from the population distribution can be
converted into a corresponding z-value
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The standard normal distribution example
If x is distributed normally with mean of 100 and standard deviation
of 50, the z-value for x = 250 is
Z = 250-100 / 50 = 3.0
This means that x = 250 is three standard deviations (3 increments
of 50 units) above the mean of 100.
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The standard normal distribution table
Provides probabilities (or areas under the normal curve) associated
with different z-values
Is constructed so that the probabilities provided represent the
chance of a value being between a positive z-value and its
population mean, 0.

Chapter 7: Introduction to Sampling Distributions
10/25/2015
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7.1 Sampling Error: What is it and Why it happens