Download 94The_Normal_Distribution Approximation of the Binomial Distribution

Chapter 9 Probability Distributions
9.4
MATHPOWERTM 12, WESTERN EDITION 9.4.1
Binomial Distribution
Both the binomial distribution and the standard normal
distribution are probability distributions. The binomial
distribution will have a shape that is similar to the
standard normal curve when
and
For both distributions, there is a mean, a standard deviation,
and the sum of its probabilities is one.
For the standard normal distribution, the
. For a binomial
distribution, these statistics will change.
The standard normal distribution is a curve, whereas the
binomial distribution is a histogram.
The shape of the standard distribution is always the same
and is symmetrical about the vertical axis. The shape of
the binomial distribution will change when the values of
and
change.
9.4.2
The Normal Distribution Approximation
If a binomial distribution has a probability of success, p,
a probability of failure, q, and there are n trials, then the
mean is
and the standard deviation is
.
9.4.3
The Normal Distribution Approximation
1. A true-false test has 40 questions. Use normal
distribution approximation to estimate the
probability of guessing 25 or more answers correctly.
9.4.4
The Normal Distribution Approximation [cont’d]
9.4.5
The Normal Distribution Approximation
2. Use normal distribution approximation to estimate
P(40 to 60 heads) when a coin is tossed 100 times.
9.4.6
The Normal Distribution Approximation
3. The probability of a student wearing running
shoes is 0.7. What is the probability that at most
25 out of 30 students are wearing running shoes?
9.4.7
The Normal Distribution Approximation
To approximate normal probabilities, follow these steps:
1. Determine the values of n, p, and q.
2. Calculate the mean and the standard deviation using
  np and   npq.
3. Using the data values, find the z-score.
4. Sketch the normal curve and shade in the appropriate
interval.
5. Use the tables or a calculator to find the area.
9.4.8
Suggested Questions:
Pages 426 and 427
2,6-10
9.4.9