The Normal Approximation to the Binomial Distribution

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Presentation transcript:

The Normal Approximation to the Binomial Distribution MDM 4U Lesson 5.6

Pascal seems normal In the situation where the probability of success is equal to 0.5 (like flipping a coin), the binomial distribution is very close to the normal distribution

20th line of Pascal's triangle 1 20 190 1140 4845 15504 38760 77520 125970 167960 184756 167960 125970 77520 38760 15504 4845 1140 190 20 1 As the number of trials increases, the binomial distribution becomes smoother and more normal.

Difference between the Normal Distribution and Binomial Distribution The binomial distribution represents discrete random variables The normal distribution is continuous, which can be represented with decimals. In order to use the normal distribution to approximate the binomial distribution, a range of values should be used, rather than the discrete values.

Mean and Standard deviation of the normal approximation to the binomial distribution If X is a binomial random variable of n independent trials, each with probability of success p, and if np > 5 and n(1-p) > 5 then the binomial random variable can be approximated by a normal distribution. MEAN: Standard Deviation:

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Practice Questions! Page 449 #1, 5, 8, 10