MATH
SC8SN

State the mathematical expression that gives the

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• apiccirello
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State the mathematical expression that gives the value of a binomial coefficient . Explain how to find the value of that expression. State the mathematical expression used to calculate the value of binomial probability . Construction Objectives: Students will be able to: Evaluate a binomial probability by using the mathematical formula for P ( X = k ). Explain the difference between binompdf(n, p, X) and binomcdf(n, p, X) . Use your calculator to help evaluate a binomial probability. If X is B (n, p ), find µ x and σ x (that is, calculate the mean and variance of a binomial distribution). Use a Normal approximation for a binomial distribution to solve questions involving binomial probability. Vocabulary: Binomial Setting – random variable meets binomial conditions Trial – each repetition of an experiment Success – one assigned result of a binomial experiment Failure – the other result of a binomial experiment PDF – probability distribution function; assigns a probability to each value of X CDF – cumulative (probability) distribution function; assigns the sum of probabilities less than or equal to X Binomial Coefficient – combination of k success in n trials Factorial – n! is n × (n-1) × (n-2) × × 2 × 1 Key Concepts: Criteria for a Binomial Setting A random variable is said to be a binomial provided: 1. The experiment is performed a fixed number of times . Each repetition is called a trial. 2. The trials are independent 3. For each trial there are two mutually exclusive (disjoint) outcomes : success or failure 4. The probability of success is the same for each trial of the experiment Most important skill for using binomial distributions is the ability to recognize situations to which they do and don’t apply Binomial PDF The probability of obtaining x successes in n independent trials of a binomial experiment, where the probability of success is p , is given by: P(x) = n C x p x (1 – p) n-x , x = 0, 1, 2, 3, …, n n C x is also called a binomial coefficient and is defined by combination of n items taken x at a time or where n! is n × (n-1) × (n-2) × × 2 × 1 n n! = -------------- k k! (n – k)! Mean and Standard Deviation: n TI-83 Support: For P(X = k) using the calculator: 2 nd VARS binompdf(n,p,k) For P(k ≤ X) using the calculator: 2 nd VARS binomcdf(n,p,k) For P(X ≥ k) use 1 – P(k < X) = 1 – P(k-1 ≤ X)

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Chapter 8: The Binomial and Geometric Distributions Example 1: Does this setting fit a binomial distribution? Explain a) NFL kicker has made 80% of his field goal attempts in the past. This season he attempts 20 field goals. The attempts differ widely in distance, angle, wind and so on. b) NBA player has made 80% of his foul shots in the past. This season he takes 150 free throws. Basketball free throws are always attempted from 15 ft away with no interference from other players.
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