MATH 321 Lecture Notes - Lecture 36: Binomial Distribution, Random Variable, Standard Deviation

• School: Ball State University
• Department: Mathematical Sciences
• Course: MATH 321
• Professor: Drew Lazar

Document Summary

Probability distribution earning objectives: approximate binomial probabilities using the normal distribution. 7. 4. 1 approximate binomial probabilities using the normal distribution (1 of 11) An experiment is said to be a binomial experiment if all of the following are true: the experiment is performed n independent times. Each repetition of the experiment is called a trial. 7. 4. 1 approximate binomial probabilities using the normal distribution (2 of 11) For a fixed p, as the number of trials n in a binomial experiment increases, the probability distribution of the random variable x becomes more nearly symmetric and bell- shaped. As a rule of thumb, if np(1 p) 10, the probability distribution will be approximately symmetric and bell-shaped. 7. 4. 1 approximate binomial probabilities using the normal distribution (3 of 11) The normal approximation to the binomial probability distribution. If np(1 p) 10, the binomial random variable x is approximately normally distributed, with mean x = np and standard deviation.