SOLUTION: 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.

Question 1197939: 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 89% of children at risk. A concerted effort was made to remove lead from the environment. Now, suppose only 16% of children in the United States are at risk of high blood-lead levels.
(a) In a random sample of 202 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 202 children taken now, what is the probability that 50 or more have high blood-lead levels? (Round your answer to three decimal places.)
Answer by ewatrrr(24785) (Show Source): You can put this solution on YOUR website!
Binomial Distribution:
Decade ago:
n = 202, p = .89 , 202*.89 and 202*.11 are > 5
mean = 202*.89 = 179.89
sd = = 4.447
NOW:
n = 202 , p = .16, 202*.16 and 202*.84 are > 5
Using the normal approximation and continuity correction factor.
(the continuity correction factor used as a Binomial Distribution is not continuous)
mean =202*.16= 32.32
sd = = 5.21
Using TI or similarly an inexpensive calculator like an Casio fx-115 ES plus
P(x ≥ 50 ) = normpdf( 49.5, 9999, 179.89,4.447)= 1
P(x ≥ 50 ) = normpdf(49.5, 9999, 32.32,5.21)= .0005

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