In the following problem, check that it is appropriate to use the normal approximation to the binomial. Then use the normal distribution to estimate the requested probabilities. More than a decade ago, high levels of lead in the blood put 80% of children at risk. A concerted effort was made to remove lead from the environment. Now, suppose only 9% of 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? (Round your answer to three decimal places.) (b) In a random sample of 200 children taken now, what is the probability that 50 or more have high blood-lead levels? (Round your answer to three decimal places.)
Continuous Probability Distributions
Probability distributions are of two types, which are continuous probability distributions and discrete probability distributions. A continuous probability distribution contains an infinite number of values. For example, if time is infinite: you could count from 0 to a trillion seconds, billion seconds, so on indefinitely. A discrete probability distribution consists of only a countable set of possible values.
Normal Distribution
Suppose we had to design a bathroom weighing scale, how would we decide what should be the range of the weighing machine? Would we take the highest recorded human weight in history and use that as the upper limit for our weighing scale? This may not be a great idea as the sensitivity of the scale would get reduced if the range is too large. At the same time, if we keep the upper limit too low, it may not be usable for a large percentage of the population!
In the following problem, check that it is appropriate to use the normal approximation to the binomial. Then use the
More than a decade ago, high levels of lead in the blood put 80% of children at risk. A concerted effort was made to remove lead from the environment. Now, suppose only 9% of children in the United States are at risk of high blood-lead levels.
(b) In a random sample of 200 children taken now, what is the probability that 50 or more have high blood-lead levels? (Round your answer to three decimal places.)
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