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Answer: Morality In a recent poll, the Gallup Organization
Chapter 7, Problem 23AYU(choose chapter or problem)
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. Suppose a survey of a random sample of 500 adult Americans is conducted in which they are asked to disclose their feelings on the overall state of moral values in the United States. Use the normal approximation to the binomial to approximate the probability that
(a) exactly 250 of those surveyed feel the state of morals is poor.
(b) no more than 220 of those surveyed feel the state of morals is poor.
(c) more than 250 of those surveyed feel the state of morals is poor.
(d) between 220 and 250, inclusive, believe the state of morals is poor.
(e) at least 260 adult Americans believe the overall state of moral values is poor. Would you find this result unusual? Why?
Questions & Answers
QUESTION:
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. Suppose a survey of a random sample of 500 adult Americans is conducted in which they are asked to disclose their feelings on the overall state of moral values in the United States. Use the normal approximation to the binomial to approximate the probability that
(a) exactly 250 of those surveyed feel the state of morals is poor.
(b) no more than 220 of those surveyed feel the state of morals is poor.
(c) more than 250 of those surveyed feel the state of morals is poor.
(d) between 220 and 250, inclusive, believe the state of morals is poor.
(e) at least 260 adult Americans believe the overall state of moral values is poor. Would you find this result unusual? Why?
ANSWER:Step 1 of 8
The normal approximation, also known as the central limit theorem (CLT) approximation, is a statistical method that uses the normal distribution to approximate the probability distribution of a random variable, even if the random variable does not follow a normal distribution. The CLT states that if a random variable is the sum of a large number of independent and identically distributed random variables, then its distribution will be approximately normal, regardless of the distribution of the individual random variables.