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 * Aim:** How do we use the normal distribution as an approximation for binomial probabilities?

At the end of the lesson, you will be able to...
 * 1) interpret the area under the bell curve as a probability
 * 2) interpret a binomial probability as a histogram and an approximation of the normal curve
 * 3) find the mean and standard deviation of a binomial distribution
 * 4) use the graphing calculator's normal cumulative density function feature (//normalcdf//) to approximate probabilities of Bernoulli trials involving "at least" and "at most".

This is a way to use the normal distribution to find probability. It's just another way of doing probability without using combinations. **We use fractions (Bernoulli's) for exact answers and we can use this method for approximation.**

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 * This video shows one way how to find probability using the graphing calculator**

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 * In this video, Len talks about using the "table". We don't use the table. Ignore "table talk" but watch the steps for entering the information into a calculator**

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 * And...one more example**


 * Classwork:** Answer the following questions. Use your graphing calculator to help you.


 * Sometimes all the information you need is not given to you. You may need to use the following to help you use the calculator:
 * 1) The mean is the number of trials(n) times the probability of successes (p)
 * 2) The standard deviation is sqrt of np(1-p)

a. Find the probability of getting at least 60 heads with 100 flips of a coin (Ans: 0.0287164928) b. The probability that a team will win a game is 3/5. Use the normal distribution to estimate the probability that the team will win at least 10 of its next 25 games. (Ans:0.9876183243)


 * Homework:** 3-23 odd. Your your graphing calculator to help you find your answers


 * [|Binom_prob.JPG]**


 * [|Binom_prob_2.JPG]**


 * Answers:**

[|A-binom_prob.JPG]


 * Journal entry:** Give an example of an experiment where it is appropriate to use a normal distribution as a approximation for a binomial probability. Explain why in this example an approximation of the probability is a better approach than finding the exact probability.