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 0.009 28-31 weeks 32-35 weeks 36 weeks 237 weeks Also assume that the probability of low birthweight is 0.947 given a gestation of <28 weeks. 0.700 given a gestation of 28-31 weeks, 0.433 given a gestation of 32-35 weeks, 0.199 given a gestation of 36 weeks, and 0.030 given a gestation of 237 weeks. (a) What is the probability of having a low birthweight infant? (Round your answer to four decimal places.) 0.010 0.052 0.038 0.891 (b) Show that the events (length of gestations 31 weeks) and (low birthweight) are not independent. (Let A (length of gestations 31 weeks) and B (low birthweight). Round your answers to four decimal places.) First we find P(AB) - Then we find P(A) - P(B) = - . Since P(AB)-Select--- P(A) - P(B), we know the events (length of gestations 31 weeks) and (low birthweight) are not independent. (c) What is the probability of having a length of gestation s36 weeks given that an infant is low birthweight? (Round your answer to four decimal places.)
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 0.009 28-31 weeks 32-35 weeks 36 weeks 237 weeks Also assume that the probability of low birthweight is 0.947 given a gestation of <28 weeks. 0.700 given a gestation of 28-31 weeks, 0.433 given a gestation of 32-35 weeks, 0.199 given a gestation of 36 weeks, and 0.030 given a gestation of 237 weeks. (a) What is the probability of having a low birthweight infant? (Round your answer to four decimal places.) 0.010 0.052 0.038 0.891 (b) Show that the events (length of gestations 31 weeks) and (low birthweight) are not independent. (Let A (length of gestations 31 weeks) and B (low birthweight). Round your answers to four decimal places.) First we find P(AB) - Then we find P(A) - P(B) = - . Since P(AB)-Select--- P(A) - P(B), we know the events (length of gestations 31 weeks) and (low birthweight) are not independent. (c) What is the probability of having a length of gestation s36 weeks given that an infant is low birthweight? (Round your answer to four decimal places.)
Chapter8: Sequences, Series,and Probability
Section8.7: Probability
Problem 4ECP: Show that the probability of drawing a club at random from a standard deck of 52 playing cards is...
Related questions
Question
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 Probability
<28 weeks
28-31 weeks
32-35 weeks
36 weeks
237 weeks
0.009
0.010
0.052
0.038
0.891
Also assume that the probability of low birthweight is 0.947 given a gestation of <28 weeks, 0.700 given a gestation of 28-31 weeks, 0.433 given a gestation of 32-35 weeks, 0.199 given a gestation of 36 weeks, and 0.030 given a gestation of 237 weeks.
(a) What is the probability of having a low birthweight infant? (Round your answer to four decimal places.)
(b) Show that the events (length of gestation ≤ 31 weeks) and (low birthweight} are not independent. (Let A = {length of gestations 31 weeks) and B = {(low birthweight}. Round your answers to four decimal places.)
First we find P(An B) =
Then we find P(A) P(B) =
Since P(AB) ---Select--- P(A) · P(B), we know the events (length of gestations 31 weeks) and (low birthweight} are not independent.
.
(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.)
Expert Solution
This question has been solved!
Explore an expertly crafted, step-by-step solution for a thorough understanding of key concepts.
This is a popular solution!
Trending now
This is a popular solution!
Step by step
Solved in 3 steps
Recommended textbooks for you
Algebra & Trigonometry with Analytic Geometry
Algebra
ISBN:
9781133382119
Author:
Swokowski
Publisher:
Cengage
Holt Mcdougal Larson Pre-algebra: Student Edition…
Algebra
ISBN:
9780547587776
Author:
HOLT MCDOUGAL
Publisher:
HOLT MCDOUGAL
Algebra & Trigonometry with Analytic Geometry
Algebra
ISBN:
9781133382119
Author:
Swokowski
Publisher:
Cengage
Holt Mcdougal Larson Pre-algebra: Student Edition…
Algebra
ISBN:
9780547587776
Author:
HOLT MCDOUGAL
Publisher:
HOLT MCDOUGAL
College Algebra (MindTap Course List)
Algebra
ISBN:
9781305652231
Author:
R. David Gustafson, Jeff Hughes
Publisher:
Cengage Learning
Calculus For The Life Sciences
Calculus
ISBN:
9780321964038
Author:
GREENWELL, Raymond N., RITCHEY, Nathan P., Lial, Margaret L.
Publisher:
Pearson Addison Wesley,