State the mathematical expression that gives the

Info icon This preview shows pages 2–4. Sign up to view the full content.

View Full Document Right Arrow Icon
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)
Image of page 2

Info iconThis preview has intentionally blurred sections. Sign up to view the full version.

View Full Document Right Arrow Icon
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.
Image of page 3
Image of page 4
This is the end of the preview. Sign up to access the rest of the document.

{[ snackBarMessage ]}

What students are saying

  • Left Quote Icon

    As a current student on this bumpy collegiate pathway, I stumbled upon Course Hero, where I can find study resources for nearly all my courses, get online help from tutors 24/7, and even share my old projects, papers, and lecture notes with other students.

    Student Picture

    Kiran Temple University Fox School of Business ‘17, Course Hero Intern

  • Left Quote Icon

    I cannot even describe how much Course Hero helped me this summer. It’s truly become something I can always rely on and help me. In the end, I was not only able to survive summer classes, but I was able to thrive thanks to Course Hero.

    Student Picture

    Dana University of Pennsylvania ‘17, Course Hero Intern

  • Left Quote Icon

    The ability to access any university’s resources through Course Hero proved invaluable in my case. I was behind on Tulane coursework and actually used UCLA’s materials to help me move forward and get everything together on time.

    Student Picture

    Jill Tulane University ‘16, Course Hero Intern