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In: Statistics and Probability

In the following problem, check that it is appropriate to use the normal approximation to the...

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 86% of children at risk. A concerted effort was made to remove lead from the environment. Now, suppose only 8% of children in the United States are at risk of high blood-lead levels. (a) In a random sample of 210 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 210 children taken now, what is the probability that 50 or more have high blood-lead levels? (Round your answer to three decimal places.)

Solutions

Expert Solution

a) A decage agro,

The probability that high levels of lead in the blood in Children at risk is , p = 0.86

The sample size is n = 210

X be the number of children who are at risk of high blood lead levels  

X ~Binomial( 210, 0.86)

Since sample Size is large binomial distribution is approximated to normal distribution

Therefore the mean is

The Standard deviation is

X ~N( 180.6 , 5.0283)

The probability that 50 or more children had high blood lead levels

b) Similarly the samples are taken now, X ~Binomial( 210, 0.08)

The mean is

The standard deviation is

The probability that 50 or more have high blood-lead levels

orchestra answered 2 years ago
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