Health:Lead Contamination More than a decade ago high levels of lead in the bloo

Question

Health:Lead Contamination More than a decade ago high levels of lead in the blood put 88% of childre at risk. A concerted effort was made to remove lead from the environment. Now, accordingly to the Third National Health and Nutrition Examination Survey(NHANES III) conducted by Center for Diseaase Control, only 9% of the children in the United States are at risk of high blood-lead levels. A) In a random sample of 200 children taken more than a decade ago, what is the probability that 50 or more had high blood-lead levels? B) In a random sample of 200 children taken now, what is the probability that 50 or more had high blood-lead levels?

Explanation / Answer

Since we have more than 30 children, we can assume that the distribution is normal.

A) A decade ago, we expect a probability of 88% with a standard deviation of sqrt(0.88*0.12/200) = 0.0230. We're looking for the probability that the test gives a result of p = 50/200 = 0.25 or greater. This corresponds to a z-score of (0.25-0.88)/(0.0230) = -27.14. So the probability is P(z > -27.14), which is approximately 1.

B) Today, we expect a probability of 9% with a standard deviation of sqrt(0.09*0.91/200) = 0.0202. We want the probability that our result is at least 0.25. This corresponds to a z-score of (0.25-0.09)/(0.0202) = 7.91. So the probability is P(z > 7.91), which is approximately 0.

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