A study tracked a cohort of very-low-birth-weight infants for twenty years. The

Question

A study tracked a cohort of very-low-birth-weight infants for twenty years. The results of the study indicated that 73% of the very-low-birth-weight babies graduated from high school during this time period. The study also reported that 84% of the comparison group of normal-birth-weight babies graduated from high school during the same period.

(a) If 40 very-low-birth-weight babies were tracked through high school, what is the probability that at least 30 will graduate from high school by age 20?

(b) If 40 normal-birth-weight babies were tracked through high school, what is the probability that at least 30 will graduate from high school by age 20?

Explanation / Answer

a)
p = 0.73
n = 40
mean = np = 40*0.73 = 29.2
std. dev. = sqrt(npq) = sqrt(40*0.73*0.27) = 2.8078

Using binomial approximation and central limit theorem,

P(X>= 30)
= P(z >= (30 - 29.2)/2.8078)
= P(z >= 0.2849)
= 0.3879

b)
p = 0.84
n = 40
mean = np = 40*0.84 = 33.6
std. dev. = sqrt(npq) = sqrt(40*0.84*0.16) = 2.3186

Using binomial approximation and central limit theorem,

P(X>= 30)
= P(z >= (30 - 33.6)/2.3186)
= P(z >= -1.5527)
= 0.9397

Related Questions

Navigate

• Browse (All)
• Browse A
• Subjects

Integrity-first tutoring: explanations and feedback only — we do not complete graded work. Learn more.