McGraw Hill Ryerson Data Management 12. Comparing and Selecting Discrete Probability Distributions

Transcription

1 .notebook McGraw Hill Ryerson Data Management 12 Comparing and Selecting Discrete Probability I am learning to compare the probability distribuons of discrete random variables solve problems involving uniform, binomial, and hypergeometric distribuons Success Criteria I will know I'm successful when I can disnguish between a discrete random variable and a connuous random variable represent a probability distribuon using a table represent a probability distribuon using a histogram calculate the expected value of a probability Click to Reveal distribuon calculate the weighted mean of a probability distribuon What are some other success criteria? 1

2 .notebook Invesgate Comparing and Hypergeometric Distribuons Consider the binomial and hypergeometric distributions. 1. If you have not already done so, drag and drop the labels below on the right to complete the compare and contrast graphic organizer. Probability of a single trial Criteria Independent n, p, q 0 to number of np Sample breakdown Dependent n, r, a 0 to number available ra/n Click here for the solution. Invesgate Comparing and Hypergeometric Distribuons 2. Reflect Use your graphic organizer from step 1 to help classify each of the probability distributions as binomial, hypergeometric, or neither. Justify your classification. Hypergeometric Neither (drag to label each probability distribuon) a) the probability of successfully shooting 13 free throws in 15 tries given the probability of success on a free throw b) the probability of a given number of rolls before rolling doubles with two dice c) the probability of each possible outcome when a card is drawn from a standard deck Neither d) selecting 25 grizzly bears at random and determining how many of them were tagged with radio chips over the last year Neither e) the probability that three or more batteries are defective in a batch of 35 batteries when batteries have a rate of defect of 0.05% Click here for the solution. 2

3 .notebook Example Compare Two Similar Distribuons a) Use the frame and labels below to create a Venn diagram to compare and contrast the following probability distributions. cutting five cards from a standard deck, with replacement, and counting the number of face cards dealing five cards at the same time from a standard deck and counting the number of face cards Hypergeometric Hypergeometric Answer Cutting Replacement, so independent Counting Successes x = 0 to 5 Dealing No replacement, so dependent # of Trials = 5 n = 52 r = 5 a = 12 Event Dealing Cutting Counting Successes x = 0 to 5 Population No replacement, so dependent Replacement, so independent Parameters # of Trials = 5 n = 52 r = 5 a = 12 Reflect R1. Is drawing 5 numbers from 49 for a lottery a binomial or hypergeometric distribution? Explain. Answer The events are dependent so drawing for a lottery is a hypergeometric distribution. R2. Sam wrote that the difference between binomial and hypergeometric distributions is that with the binomial distribution each trial has the same probability, but with hypergeometric the individual probabilities change with the sampling. Is this an accurate statement? Explain. No,Sam's statement would be more accurate if it said "with hypergeometric the individual probabilities change with the lack of replacement." Answer 3

4 .notebook 1 Use the pen tool to choose the best answer. Which situation would be represented by a binomial distribution? A Dealing 2 cards from a standard deck B The top face showing when rolling a single die C Drawing one letter tile from a bag of 50 eight times, with replacement. D Recording the Probability of Precipitation (P.O.P.) for 7 days. Answer C 2 Use the pen tool to choose the best answer. Which situation would be represented by a uniform distribution? A Dealing 2 cards from a standard deck B The top face showing when rolling a single die C Drawing one letter tile from a bag of fifty eight times, with replacement. D Recording the Probability of Precipitation (P.O.P.) for 7 days. Answer B 4

5 .notebook 3 Use the pen tool to choose the best answer. Which situation would be represented by a hypergeometric distribution? A Dealing 2 cards from a standard deck B The top face showing when rolling a single die C Drawing one letter tile from a bag of fifty eight times, with replacement. D Recording the Probability of Precipitation (P.O.P.) for 7 days. Answer A The following pages contain solutions for the previous questions. 5

6 .notebook Solutions Invesgate Comparing and Hypergeometric Distribuons Finite Population Continuous Counting successes Set number of Random variable is the number of successes Independent Probability of a single trial np n, p, q 0 to number of Dependent Sample breakdown ra/n n, r, a 0 to number available Go back to the question Solutions Invesgate Comparing and Hypergeometric Distribuons 2. a) the probability of successfully shooting 13 free throws in 15 tries given the probability of success on a free throw ; the successful free throws are counted, and each free throw is independent. b) the probability of a given number of rolls before rolling doubles with two dice Neither; even though the are independent, there is no set number of. c) the probability of each possible outcome when a card is drawn froma standard deck Neither; it is a single draw of a card. d) selecting 25 grizzly bears at random and determining how many of them were tagged with radio chips over the last year Hypergeometric; are dependent and we are counng successes (tagged bears). e) the probability that three or more batteries are defective in a batch of 35 batteries when batteries have a rate of defect of 0.05% ; we are counng successes (number of defecve baeries) in a set number of independent. Go back to the question 6

7 Attachments Ex1.xlsx