(a)
p=0.87, q=0.13, n=212
need P(X>=50)
mean = np = 212*0.87 = 184.44
variance = npq = 23.9772
σ = sqrt(variance) = 4.8967
To find
P(X>=50)=P(Z>(50-184.44)/4.8967)
=P(Z>-27.45)=1.000 from Normal probability table.
Do a similar calculation for (b) using p=0.13
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 13% of children in the United States are at risk of high blood-lead levels.
(a) In a random sample of 212 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 212 children taken now, what is the probability that 50 or more have high blood-lead levels? (Round your answer to three decimal places.)
Very frustrating- found the np, nq, mean, standard deviation, z, and the result is too big to find on the number chart.
1 answer