Lecture 10

# Lecture 10 - p(x = 0 = What is the probability that at most...

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BINOMIAL PROBABILITY DISTRIBUTIONS Conditions: The experiment involves a sequence of n identical trials. Each trial has only two possible outcomes, denoted as success or as failure. The probability of getting a success, p, is constant throughout the trials. The probability of getting a failure, q = 1 - p, is also constant throughout the trials. Each trial is independent of the previous trials. The binomial distribution is a discrete distribution.

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Examples of binomial experiments: Flipping a coin Quality control (defective or nondefective products) True-False questions on exams Multiple choice questions (correct or incorrect answers) Binomial Probability Function: for x = 0, 1, 2, …, n ( 29 ) ( ) 1 ( ) ( x n x n x p p X P - - =
The probability that a dog has a reaction to a certain shampoo is .4. Suppose 3 dogs are given the shampoo. Let the random variable X be the number of dogs that have a reaction. p(x) = 3 C x (.4) x (1-.4) (3-x) for x = 0, 1, 2, 3 What is the probability that no dogs will react to the shampoo?

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Unformatted text preview: p(x = 0) = What is the probability that at most two dogs react to the shampoo? What is the probability that exactly 1 dog reacts to the drug? MEAN, VARIANCE AND STANDARD DEVIATION OF A BINOMIAL DISTRIBUTION *mean is also called the expected value Mean: μ = E(X) = np Variance: σ 2 = np(1-p) = npq The standard deviation, σ , is the square root of the variance. Example 1: Find the mean and Stdev For the dog reaction example, Example 2: The probability of success on a single trial of a binomial experiment is known to be ¼. The random variable X has a mean value of 80. Find the number of trials involved in this experiment and the standard deviation of X. Example 3: The probability that a hunter hits a target is .7. If 8 shots are fired, find the probability that: He will hit the target 4 times. He will hit the target at least once. He will miss the target every time. How many times should he expect to hit the target?...
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## This note was uploaded on 02/15/2009 for the course STAT 2004 taught by Professor Melutz during the Fall '07 term at Virginia Tech.

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Lecture 10 - p(x = 0 = What is the probability that at most...

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