Check for Understanding
Check for Understanding 1. List out the 4 characteristics of a binomial distribution
2. List out the 4 characteristics of a geometric distribution
3. Identify the binomial experiment in the following group of statements: a) a shopping mall is interested in the income levels of its customers and is taking a survey to gather information b) a business firm introducing a new product wants to know how many purchases its clients will make each year c) a sociologist is researching an area in an effort to determine the proportion of households with male "head of household" d) a study is concerned with the average hours worked by teenagers who are attending high school
Answers 1. Characteristics of Binomial Setting(1) Each observation falls into one of just two categories, such as “success” or “failure.” (2) There is a fixed number n of observations (3) The observations are all independent. That is, knowing the result of one observation tells you nothing about the other observation. (3) The probability of a success, call it p, is the same for each observation. 2. Characteristics of Geometric Setting(1) Each observation falls into one of just two categories, such as “success” or “failure.” (2) The observations are all independent. (3) The probability of a success, call it p, is the same for each observation. (4) The variable of interest is the number of trials required to obtain the first success. The last characteristic is what distinguishes this from binomial distributions!!! 3. The correct answer is C. In answer C, there are only two possible answers: “Yes” meaning there is a male head-ofhousehold, or “No” meaning there is NOT a male head-ofhousehold. All the other options have more than two possible responses and are therefore not Binomial.
2. List out the 4 characteristics of a geometric distribution
3. Identify the binomial experiment in the following group of statements: a) a shopping mall is interested in the income levels of its customers and is taking a survey to gather information b) a business firm introducing a new product wants to know how many purchases its clients will make each year c) a sociologist is researching an area in an effort to determine the proportion of households with male "head of household" d) a study is concerned with the average hours worked by teenagers who are attending high school
Answers 1. Characteristics of Binomial Setting(1) Each observation falls into one of just two categories, such as “success” or “failure.” (2) There is a fixed number n of observations (3) The observations are all independent. That is, knowing the result of one observation tells you nothing about the other observation. (3) The probability of a success, call it p, is the same for each observation. 2. Characteristics of Geometric Setting(1) Each observation falls into one of just two categories, such as “success” or “failure.” (2) The observations are all independent. (3) The probability of a success, call it p, is the same for each observation. (4) The variable of interest is the number of trials required to obtain the first success. The last characteristic is what distinguishes this from binomial distributions!!! 3. The correct answer is C. In answer C, there are only two possible answers: “Yes” meaning there is a male head-ofhousehold, or “No” meaning there is NOT a male head-ofhousehold. All the other options have more than two possible responses and are therefore not Binomial.
