We appreciate your visit to 22 Morality In a recent poll the Gallup Organization found that 45 of adult Americans believe that the overall state of moral values in the. This page offers clear insights and highlights the essential aspects of the topic. Our goal is to provide a helpful and engaging learning experience. Explore the content and find the answers you need!
Answer :
The probability that exactly 250 of those surveyed feel the state of morals is poor is approximately 0.9918.
(To find the probability that exactly 250 of those surveyed feel the state of morals is poor, we can use the normal approximation to the binomial with mean np = 500 * 0.45 = 225 and standard deviation √(npq) = √(500 * 0.45 * 0.55) ≈ 10.42, where q = 1 - p.
Then, we can standardize the value of 250 using the formula z = (x - np) / √(npq), where x is the number of people who feel the state of morals is poor.
z = (250 - 225) / 10.42 ≈ 2.4
Using a standard normal table or calculator, we find that the probability of z being less than or equal to 2.4 is approximately 0.9918.
Therefore, the probability that exactly 250 of those surveyed feel the state of morals is poor is approximately 0.9918.
(b) To find the probability that no more than 220 of those surveyed feel the state of morals is poor, we can use the normal approximation to the binomial with mean np = 500 * 0.45 = 225 and standard deviation √(npq) = √(500 * 0.45 * 0.55) ≈ 10.42, where q = 1 - p.
Then, we can standardize the value of 220 using the formula z = (x - np) / √(npq), where x is the number of people who feel the state of morals is poor.
z = (220 - 225) / 10.42 ≈ -0.48
Using a standard normal table or calculator, we find that the probability of z being less than or equal to -0.48 is approximately 0.3146.
Therefore, the probability that no more than 220 of those surveyed feel the state of morals is poor is approximately 0.3146.
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