By recognizing that your data set consists of smokers and nonsmokers, you gain tremendous power in extending conclusions beyond the data by recognizing that these events are mutually exclusive (or disjoint) outcomes. Furthermore, because each individual can be considered independent of each other and the probability of each youth smoking is the same, you can represent such a random variable X using a binomial probability distribution. Suppose the following validation study is to be completed using 8 randomly selected youth from the East Boston area, where p represents the probability of selecting a smoker from the sample. Use the probability of randomly selecting a smoker from the full data set: p = the probability of selecting a smoker in this sample. to represent Complete the following table for this binomial probability distribution using the binomial formula to determine the missing values. P(X = 0) %3D P(X = 1) P(X = 2) 17 8. 6. 0.0000 0.0000 0.0000 01 1 3 P(X) 0.0331 0.0046 0.0004 Now use the table to determine the following values: 1. Calculate the probability that fewer than 2 of the 8 randomly selected children are smokers. 2. Would it be considered statistically unusual if more than 2 out of the 8 randomly selected children were found to be smokers? Compute the probability and explain why or why not. 3. Calculate the probability that none of the 8 randomly selected children is a smoker. 4. Calculate the probability that at least one of the 8 randomly selected children is a smoker. 5. Describe the relationship between the results of Questions 3 and 4. How many youths would you expect to be smokers in such a random sample of 8 youths? By recognizing that your data set consists of smokers and nonsmokers, you gain tremendous power in extending conclusions beyond the data by recognizing that these events are mutually exclusive (or disjoint) outcomes. Furthermore, because each individual can be considered independent of each other and the probability of each youth smoking is the same, you can represent such a random variable X using a binomial probability distribution. Suppose the following validation study is to be completed using 8 randomly selected youth from the East Boston area, where p represents the probability of selecting a smoker from the sample. Use the probability of randomly selecting a smoker from the full data set: p = the probability of selecting a smoker in this sample. to represent Complete the following table for this binomial probability distribution using the binomial formula to determine the missing values. P(X = 0) %3D P(X = 1) P(X = 2) 17 8. 6. 0.0000 0.0000 0.0000 01 1 3 P(X) 0.0331 0.0046 0.0004 Now use the table to determine the following values: 1. Calculate the probability that fewer than 2 of the 8 randomly selected children are smokers. 2. Would it be considered statistically unusual if more than 2 out of the 8 randomly selected children were found to be smokers? Compute the probability and explain why or why not. 3. Calculate the probability that none of the 8 randomly selected children is a smoker. 4. Calculate the probability that at least one of the 8 randomly selected children is a smoker. 5. Describe the relationship between the results of Questions 3 and 4. How many youths would you expect to be smokers in such a random sample of 8 youths? By recognizing that your data set consists of smokers and nonsmokers, you gain tremendous power in extending conclusions beyond the data by recognizing that these events are mutually exclusive (or disjoint) outcomes. Furthermore, because each individual can be considered independent of each other and the probability of each youth smoking is the same, you can represent such a random variable X using a binomial probability distribution. Suppose the following validation study is to be completed using 8 randomly selected youth from the East Boston area, where p represents the probability of selecting a smoker from the sample. Use the probability of randomly selecting a smoker from the full data set: p = the probability of selecting a smoker in this sample. to represent Complete the following table for this binomial probability distribution using the binomial formula to determine the missing values. P(X = 0) %3D P(X = 1) P(X = 2) 17 8. 6. 0.0000 0.0000 0.0000 01 1 3 P(X) 0.0331 0.0046 0.0004 Now use the table to determine the following values: 1. Calculate the probability that fewer than 2 of the 8 randomly selected children are smokers. 2. Would it be considered statistically unusual if more than 2 out of the 8 randomly selected children were found to be smokers? Compute the probability and explain why or why not. 3. Calculate the probability that none of the 8 randomly selected children is a smoker. 4. Calculate the probability that at least one of the 8 randomly selected children is a smoker. 5. Describe the relationship between the results of Questions 3 and 4. How many youths would you expect to be smokers in such a random sample of 8 youths? By recognizing that your data set consists of smokers and nonsmokers, you gain tremendous power in extending conclusions beyond the data by recognizing that these events are mutually exclusive (or disjoint) outcomes. Furthermore, because each individual can be considered independent of each other and the probability of each youth smoking is the same, you can represent such a random variable X using a binomial probability distribution. Suppose the following validation study is to be completed using 8 randomly selected youth from the East Boston area, where p represents the probability of selecting a smoker from the sample. Use the probability of randomly selecting a smoker from the full data set: p = the probability of selecting a smoker in this sample. to represent Complete the following table for this binomial probability distribution using the binomial formula to determine the missing values. P(X = 0) %3D P(X = 1) P(X = 2) 17 8. 6. 0.0000 0.0000 0.0000 01 1 3 P(X) 0.0331 0.0046 0.0004 Now use the table to determine the following values: 1. Calculate the probability that fewer than 2 of the 8 randomly selected children are smokers. 2. Would it be considered statistically unusual if more than 2 out of the 8 randomly selected children were found to be smokers? Compute the probability and explain why or why not. 3. Calculate the probability that none of the 8 randomly selected children is a smoker. 4. Calculate the probability that at least one of the 8 randomly selected children is a smoker. 5. Describe the relationship between the results of Questions 3 and 4. How many youths would you expect to be smokers in such a random sample of 8 youths?