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Chapter 9: The Normal Probability Distribution
Notes:
In solving application problems relating to the normal distribution, it may be
helpful if you use the following procedure:
Define the appropriate normal variable with appropriate parameters
(mean and standard deviation).
Write out an appropriate probability statement.
Draw a normal curve.
Analyze and shade in the desired area.
Use the Normal Distribution EXCEL workbook to help with the
computations.
If you want to use the normal distribution table, then you need to write
out an equivalent transformed probability statement using the z-score.
Use the standard normal distribution table to find the shaded area.
Next we will discuss how we can approximate the binomial probability
distribution with the normal distribution.
Section Review
9-6 The Normal Approximation to the Binomial Distribution
Recall from
Section 9-2
that simulations were presented in which one can
view the normal distribution as the limiting distribution of a binomial
random variable.
Based on the observations from
Figures 9-2
to
9-4 in Section 9-2
, we can
generally say that as the sample size increases, the distribution for the
binomial random variable will converge to the normal distribution. The rate
of convergence will depend on the probability
p
of success for the binomial
random variable in the binomial experiment.
e-Self Review