ified by length of gestation in the following five categories: <28 weeks, 28-31 "ferent periods of gestation are as given in the table below. gestation Probability 0.006 "eeks wweeks. weeks eeks weeks 0.010 0.049 0.035 0.900 probabilities are given: assume that the probability of low birthweight is 0.948 given a gestation of <28 weeks, iven a gestation of 32-35 weeks, 0.202 given a gestation of 36 weeks, and 0.028 given a gestation of 237 wee mility of having a low birthweight infant? (Round your answer to four decimal places. Hint: Use the Law of Total R ants (length of gestation s 31 weeks) and (low birthweight) are not independent. (Let A (length of gestation ht). Round your answers to four decimal places. Hint: sketch out the contingency table with rows as length of Not Low Birthweight".) x Since P(An B) ✔ P(A) B)- X.Then we find P(A) P(B) en s 31 weeks) and (low birthweight) are not independent. bility of having a length of gestation $36 weeks given that an infant is low birthweight? (Round your answer t
ified by length of gestation in the following five categories: <28 weeks, 28-31 "ferent periods of gestation are as given in the table below. gestation Probability 0.006 "eeks wweeks. weeks eeks weeks 0.010 0.049 0.035 0.900 probabilities are given: assume that the probability of low birthweight is 0.948 given a gestation of <28 weeks, iven a gestation of 32-35 weeks, 0.202 given a gestation of 36 weeks, and 0.028 given a gestation of 237 wee mility of having a low birthweight infant? (Round your answer to four decimal places. Hint: Use the Law of Total R ants (length of gestation s 31 weeks) and (low birthweight) are not independent. (Let A (length of gestation ht). Round your answers to four decimal places. Hint: sketch out the contingency table with rows as length of Not Low Birthweight".) x Since P(An B) ✔ P(A) B)- X.Then we find P(A) P(B) en s 31 weeks) and (low birthweight) are not independent. bility of having a length of gestation $36 weeks given that an infant is low birthweight? (Round your answer t
A First Course in Probability (10th Edition)
10th Edition
ISBN:9780134753119
Author:Sheldon Ross
Publisher:Sheldon Ross
Chapter1: Combinatorial Analysis
Section: Chapter Questions
Problem 1.1P: a. How many different 7-place license plates are possible if the first 2 places are for letters and...
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Transcribed Image Text:Obstetrics
Suppose that infants are classified as low birthweight if they have a birthweight <2,500 g and as normal birthweight if they have a birthweight 22,500 g. Suppose
that infants are also classified by length of gestation in the following five categories: <28 weeks, 28-31 weeks, 32-35 weeks, 36 weeks, and 237 weeks. Assume
the probabilities of the different periods of gestation are as given in the table below.
Length of gestation
<28 weeks
Probability.
0.006
0.010
28-31 weeks
32-35 weeks
36 weeks
0.035
237 weeks
0.900
The following conditional probabilities are given: assume that the probability of low birthweight is 0.948 given a gestation of <28 weeks, 0.700 given a gestation
of 28-31 weeks, 0.432 given a gestation of 32-35 weeks, 0.202 given a gestation of 36 weeks, and 0.028 given a gestation of 237 weeks.
(a) What is the probability of having a low birthweight infant? (Round your answer to four decimal places. Hint: Use the Law of Total Probability.)
0.06612
0.049
(b) Show that the events (length of gestation ≤ 31 weeks) and (low birthweight) are not independent. (Let A (length of gestation s 31 weeks) and
B (low birthweight). Round your answers to four decimal places. Hint: sketch out the contingency table with rows as length of gestation and columns as
"Low Birthweight, Not Low Birthweight".)
First we find P(An B)=
x Then we find P(A) - P(B) -
(length of gestation s 31 weeks) and (low birthweight) are not independent.
X Since P(An B)
P(A) P(8), we know the events
(c) What is the probability of having a length of gestation $36 weeks given that an infant is low birthweight? (Round your answer to four decimal places.)
x
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