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

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 87% 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 186 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 186 children taken now, what is the probability that 50 or more have high blood-lead levels? (Round your answer to three decimal places.)

Explanation / Answer

given n = 186

p=.87, q=1-p=.13 r=50,

P^ = r/n = 50/186=0.2688

standard deviation = sqrt (pq/n)= sqrt(*0.87*0.13)/186) = 0.02465

Now Z =( 0.2688-0.87)/0.0246 = -24.1

looking at z table as its greater value so its equal to 1 or 100 % probability

b) p=8%=0.08 q =0.92 n =186

P^=0.2688

standard deviation = sqrt(pq/n)=0.0198

Z= (0.2688-0.08)/0.0198= 9.535

again a big number so probality is 1

now more than it is 1 -1 =0

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