Chapter 8 Binomial and Geometric Distributions Binomial vs. Geometric Chapter 8 Binomial and Geometric Distributions

Binomial vs. Geometric The Binomial Setting The Geometric Setting Each observation falls into one of two categories. 1. Each observation falls into one of two categories. The probability of success is the same for each observation. 2. The probability of success is the same for each observation. The observations are all independent. The observations are all independent. There is a fixed number n of observations. 4. The variable of interest is the number of trials required to obtain the 1st success.

Working with probability distributions State the distribution to be used Define the variable State important numbers Binomial: n & p Geometric: p

X = # of people use express Twenty-five percent of the customers entering a grocery store between 5 p.m. and 7 p.m. use an express checkout. Consider five randomly selected customers, and let X denote the number among the five who use the express checkout. binomial n = 5 p = .25 X = # of people use express

What is the probability that two used express checkout? binomial n = 5 p = .25 X = # of people use express

What is the probability that at least four used express checkout? binomial n = 5 p = .25 X = # of people use express

X = # of people who believe… “Do you believe your children will have a higher standard of living than you have?” This question was asked to a national sample of American adults with children in a Time/CNN poll (1/29,96). Assume that the true percentage of all American adults who believe their children will have a higher standard of living is .60. Let X represent the number who believe their children will have a higher standard of living from a random sample of 8 American adults. binomial n = 8 p = .60 X = # of people who believe…

Interpret P(X = 3) and find the numerical answer. binomial n = 8 p = .60 X = # of people who believe The probability that 3 of the people from the random sample of 8 believe their children will have a higher standard of living.

X = # of people who believe Find the probability that none of the parents believe their children will have a higher standard. binomial n = 8 p = .60 X = # of people who believe

Developing the Geometric Formula X Probability

The Mean and Standard Deviation of a Geometric Random Variable If X is a geometric random variable with probability of success p on each trial, the expected value of the random variable (the expected number of trials to get the first success) is

X = # of disc drives till defective Suppose we have data that suggest that 3% of a company’s hard disc drives are defective. You have been asked to determine the probability that the first defective hard drive is the fifth unit tested. geometric p = .03 X = # of disc drives till defective

X = # of free throws till miss A basketball player makes 80% of her free throws. We put her on the free throw line and ask her to shoot free throws until she misses one. Let X = the number of free throws the player takes until she misses. geometric p = .20 X = # of free throws till miss

What is the probability that she will make 5 shots before she misses? geometric p = .20 X = # of free throws till miss What is the probability that she will miss 5 shots before she makes one? geometric p = .80 Y = # of free throws till make

X = # of free throws till miss What is the probability that she will make at most 5 shots before she misses? geometric p = .20 X = # of free throws till miss