5-2 Binomial Probability Distributions 227 Statistical Literacy and Critical Thinking 1. Movies When randomly selecting a speaking character in a movie, the probability of getting a female is 0.331 (based on data from “Inequality in 1200 Popular Films,” by Smith, et al., Annenberg Foundation). If we want to find the probability that among five randomly selected speaking characters in movies, there are exactly two females, what is wrong with this solution: P12 females among 5 speaking characters2 = P1female2 # P1female2 # P1male2 # P1male2 # P1male2 = 10.331210.331211 - 0.331211 - 0.331211 - 0.3312 = 0.0328 2. Notation Assume that we want to find the probability that when five speaking characters in movies are randomly selected, exactly two of them are females. Also assume that when randomly selecting a speaking character in a movie, the probability of getting a female is 0.331. Identify the values of n, x, p, and q. 3.Independent Events Again assume that when randomly selecting a speaking character in a movie, the probability of getting a female is 0.331, as in Exercise 1. If we want to find the probability of 20 females when 50 different speaking characters are randomly selected from a population of 1500 speaking characters, are the 50 selections independent? Using the 5% guideline for cumbersome calculations, can they be treated as being independent? 4.Notation of 0+ Using the same survey described in Exercise 1, the probability of randomly selecting 50 speaking characters from movies and getting 40 females is expressed as 0+. Does 0+ indicate that it is impossible to get 40 females among the 50 speaking characters? What does 0+ indicate? Identifying Binomial Distributions. In Exercises 5–12, determine whether the given procedure results in a binomial distribution or a distribution that can be treated as binomial (by applying the 5% guideline for cumbersome calculations). For those that are not binomial and cannot be treated as binomial, identify at least one requirement that is not satisfied. 5.Pew Survey In a Pew Research Center survey of 3930 subjects, the ages of the respondents are recorded. 6.Pew Survey In a Pew Research Center survey, 3930 subjects were asked if they have ever fired a gun, and the responses consist of “yes” or “no.” 7. LOL In a U.S. Cellular survey of 500 smartphone users, subjects are asked if they find abbreviations (such as LOL or BFF) annoying, and each response was recorded as “yes,” “no,” or “not sure.” 8.Clinical Trial of YSORT The YSORT method of gender selection, developed by the Genetics & IVF Institute, was designed to increase the likelihood that a baby will be a boy. When 291 couples use the YSORT method and give birth to 291 babies, the genders of the babies are recorded. 9.Surveying Senators The Senate members of the 116th Congress include 75 males and 25 females. Forty different senators are randomly selected without replacement, and the gender of each selected senator is recorded. 10.Surveying Senators Ten different senators from the 116th Congress are randomly selected without replacement, and the numbers of terms that they have served are recorded. 11.Smart TV In a comScore survey, 3600 different households were randomly selected without replacement, and respondents were asked whether the household had a smart TV. Answers of “yes” and “no” were recorded. 12. Credit Cards In a CreditCards.com survey, 1659 different adults with credit cards were randomly selected without replacement, and respondents were asked if they have ever changed their primary credit card. Responses of “yes” and “no” were recorded. 5-2 Basic Skills and Concepts
RkJQdWJsaXNoZXIy NjM5ODQ=