Question

1. The following data are derived from the 1973 Final Natality Statistics Report issued by the National Center for Health Statistics. Report issued by the National Center for Health Statistics. These data are for live births only. Suppose that infants are classified as low birthweight if the infant is ≤ 2500 grams, normal birthweight is > 2500 grams. Furthermore, assume gestation period can be classified as less than 20 weeks (< 20), 20 or more weeks to less than 28 weeks [20,28), 28 or more weeks to less than 36 weeks [28,36),and 36 or more weeks (≥36). The table below presents the probability of each gestational period and the probability of low birth weight given that length of gestational period. (40 points)

Gestation Length	P(Gestation Length)	P(LBW|Gestation Length
< 20 weeks	.0004	P(LBW|<20 weeks) = 0.813
[20,28)weeks	.0059	P(LBW|[20,28)weeks) = 0.541
[28,36) weeks	.0855	P(LBW|[28,36)weeks) = 0.379
≥ 36 weeks	.9082	P(LBW|≥ 36 weeks) = 0.035

1. What is the probability of a low birth weight child? (10 points)
2. Given the child is LBW, what is the probability the gestational period was < 28 weeks? (25 points)

Answer 1

a)

Probability of low birth weight = P( each gestation period ) * P (LBW)

P(gestation)	P(LBW)	P(gestation) * P(LBW)
0.0004	0.813	0.000325
0.0059	0.541	0.003192
0.0855	0.379	0.032405
0.9082	0.035	0.031787
	Total	0.0677

2)

We have to now calculate = P(gestation <20 |LBW)

From baye's theorem

P (gestation <20 |LBW) = P(LBW| gestation <20)   * P(gestation <20) / P(LBW)

= 0.813 * 0.0004 / 0.0677

= 0.004803

P (gestation <[20,28) |LBW) = P(LBW| gestation [20,28))   * P(gestation [20,28)) / P(LBW)

= 0.541* .0059 / 0.0677

= 0.04714

Total = 0.004803 + 0.04714 = 0.051943

Please let me know in case of any doubt.