Question

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.)

Answer 1

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