Survey
* Your assessment is very important for improving the workof artificial intelligence, which forms the content of this project
* Your assessment is very important for improving the workof artificial intelligence, which forms the content of this project
Math Tech IIII, Nov 18 The Binomial Distribution III Book Sections: 4.2 Essential Questions: How can I compute the probability of any event? How can I create a discrete binomial probability distribution and how do I compute binomial statistics? Standards: DA-5.6, S.MD.1, .2, .3 The Universal First Step • Identify n, p, and x (if it applies) or all possible values of x in your problem. p may be given or it may not. If not, enough information will be given to figure it out. Either way, you must have p. • Important point – no one is ever going to give you q. If you need it, YOU are going to have to find it. How? q=1-p Remember • In a discrete probability distribution, which a binomial distribution is, the expected value and the mean are the same thing. Binomial Probability Distributions • Creating a discrete binomial probability distribution: To construct a binomial distribution table, open STAT Editor 1) type in 0 to n in L1 2) Move cursor to top of L2 column (so L2 is hi lighted) 3) Type in command binomialpdf(n, p, L1) and L2 gets the probabilities. Example Produce a binomial probability distribution for n = 8, p = 0.54, and x = 0 – 8. Put 0 – 8 into L1 Place cursor on name of L1 Type in binomialpdf(8, .54, L1) The result Example 1 • Produce a discrete binomial probability distribution for the following: n = 4, p = 0.53. • Use as much of the template as required to build your distribution. X P(x) Example 1a • Three in five beagle puppies have their eyes open within 7 days of their birth. James’ beagle had a litter of 6 pups 7 days ago. Produce a discrete probability distribution for this binomial experiment. X P(x) 0 1 2 3 4 5 6 Binomial Statistics • Because of the nature of this distribution, binomial mean, variance, and standard deviation are almost trivial. Here are the formulas: Mean μ = np σ2 = npq Variance σ = npq Standard deviation One other pearl of wisdom – You could always compute mu (μ) and sigma (σ) using the 1-var stat L1, L2 computation on the calculator {providing you have the distribution in L1 and L2} How Do You Do It? • To compute binomial statistics: 1. Find n, p, and q 2. Plug and chug into the formulas: μ = np σ2 = npq σ = npq Mean Variance Standard deviation Modified Formulas for Less Fun Mean, there is no changing this one μ = np Variance, forget about it. σ2 = npq σ = (n p (1 p)) .5 Standard deviation, put it on the calculator just like this. Now you only need n and p. Example 2 • An archer has an 80% chance of hitting a target at 50 yards. The archer shoots 5 arrows. What are the mean and standard deviation of the probability distribution for this situation? Example 3 • In Phoenix, Arizona, about 92% of the days in a year are sunny. Find the mean and standard deviation of the number of sunny days during the month of February. Example 4 • The 2010 census has concluded that 16% of American households own 2 or more pets. What is the mean and standard deviation of the number of American households out of 12 that would have two pets? Example 1a, The Other Way • Three in five beagle puppies have their eyes open within 7 days of their birth. James’ beagle had a litter of 6 pups 7 days ago. Produce a discrete probability distribution for this binomial experiment. X P(x) 0 1 2 3 4 5 6 Final Thought • Probability is, was, and will be a number between 0 and 1, it can be 0 and it can be 1. Computing Probability • There are 5 computations you need to know how to accomplish in binomial probability which are: x = #, x < #, x > #, x ≤ # and x ≥ # • Use the computation sheet in any probability to set the problem up • How will you know that you are computing a probability? Answer – The problem will say it. Classwork: CW 11/18/16, 1-12 Homework – None