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 90% of children at risk. A concerted effort was made to remove lead from the environment. Now, suppose only 14% 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)_

n=	210	p=	0.9000
here mean of distribution=μ=np=		189
and standard deviation σ=sqrt(np(1-p))=		4.3474
for normal distribution z score =(X-μ)/σx
therefore from normal approximation of binomial distribution and continuity correction:

probability that 50 or more had high blood-lead levels :

probability =

P(X>49.5)

=

P(Z>-32.09)=

1-P(Z<-32.09)=

1-0=

1.000

b)

here mean of distribution=μ=np=		29.4
and standard deviation σ=sqrt(np(1-p))=		5.0283

probability =

P(X>49.5)

=

P(Z>4)=

1-P(Z<4)=

1-1=

0.000