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 89% of children at risk. A concerted effort was made to remove lead from the environment. Now, suppose only 13% of children in the United States are at risk of high blood-lead levels.
(a) In a random sample of 204 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 204 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. Mu = np = .89(204) = 181.56

p(r => 49.5)
sd = 4.469

z = (49.5-181.56)/4.469 =

b
mu = .13(204) = 26.52
Sd = 4.803
z = (49.5-26.52)/4.80 = 4.7875