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 198 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 198 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) In a random sample of 198 children taken more than a decade ago,

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

n=198 , p = 0.90

np=198*0.90 = 17.82 > 10

n(1-p) = 198*(1-0.90) = 19.8>10

Therefore, we can use here, use the normal approximation to the binomial.

...............using continuity correction

=P[Z>7.50]

  

=1-1................using normal probability table.

=0

(b) In a random sample of 198 children taken now,

the probability that 50 or more have high blood-lead levels

n=198, p=0.14

np=198 * 0.14 = 27.72 > 10

n(1-p) = 198*(1-0.14) =170.28 > 10

  

=P[Z>4.46]

  

=1-1.................using normal probability table.

=0