1. MATHPOWER TM 12, WESTERN EDITION Chapter 9 Probability Distributions 9.4 9.4.1

2. 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. Binomial Distribution 9.4.2

3. 9.4.3 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.

4. 9.4.4 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.

5. 9.4.5 The Normal Distribution Approximation [cont’d]

6. 9.4.6 The Normal Distribution Approximation 2. Use normal distribution approximation to estimate P(40 to 60 heads) when a coin is tossed 100 times.

7. 9.4.7 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?

8. 9.4.8 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 and 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. Suggested Questions: Pages 426 and 427 2,6-10 9.4.9