Math Problem Statement
In a recent poll, the Gallup Organization found that 45% of adult Americans believe that the overall state of moral values in the United States is poor. If a survey of a random sample of 15 adults in this country is conducted in which they are asked to disclose their feelings on the overall state of moral values In 100 trials of this experiment, we expect about enter your response here to result in exactly 8 adults who feel the state of morals is poor. (Round to the nearest whole number as needed.)
Solution
We can model this scenario using a binomial distribution because we have a fixed number of independent trials (15 adults), each with two possible outcomes: an adult either believes the moral values are poor or they do not. The probability of success (an adult believing the state of morals is poor) is given as 45%, or (
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Math Problem Analysis
Mathematical Concepts
Probability
Binomial Distribution
Formulas
P(X = k) = C(n, k) * p^k * (1 - p)^(n - k)
Expected Value = n * p
Theorems
Binomial Theorem
Law of Large Numbers
Suitable Grade Level
Grades 11-12
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