Birth Weights in America The National Center for Health Statistics (NCHS) keeps
ID: 2909475 • Letter: B
Question
Birth Weights in America
The National Center for Health Statistics (NCHS) keeps records of many health-related aspects of people, including the birth weights of all babies born in the United States. The birth weight of a baby is related to its gestation period (the time between conception and birth). For a given gestation period, the birth weights can be approximated by a normal distribution.
The means and standard deviations of the birth weights of the birth weights for various gestation periods are shown in the table below. One of the goals of the NCHS is to reduce the percentage of babies born with low birth weights. However, the problem of low birth weights increased from the 1990's to the 2000's.
Using the table below, answer all of the questions that follow. Make sure that you show your work and explain your reasoning.
Gestation Period
Mean Birth Weight (#)
Standard Deviation (#)
under 28 wks
1.9
1.22
28-31 weeks
4.12
1.87
32-33 weeks
5.14
1.57
34-36 weeks
6.19
1.29
37-39 weeks
7.29
1.08
40 weeks
7.66
1.04
41 weeks
7.75
1.07
42 weeks and over
7.57
1.11
For each problem:
Show all your work.
Include the name of the software you used, the function, and the inputs to it.
Express any probabilities rounded to 3-significant digits.
Explain what each of your results means.
4. A birth weight of less than 3.25 pounds is classified by NCHS as a "very low birth weight." What is the probability that a baby has a very low birth weight for each of the following gestation periods?
(a) under 28 weeks
(b) 28 to 31 weeks
(c) 32 to 33 weeks
(d) 37 to 39 weeks
Gestation Period
Mean Birth Weight (#)
Standard Deviation (#)
under 28 wks
1.9
1.22
28-31 weeks
4.12
1.87
32-33 weeks
5.14
1.57
34-36 weeks
6.19
1.29
37-39 weeks
7.29
1.08
40 weeks
7.66
1.04
41 weeks
7.75
1.07
42 weeks and over
7.57
1.11
Explanation / Answer
Z = (X - mean)/sd
P(X < 3.25) = P( Z < (3.25 - mean)/sd)
(a) under 28 weeks
mean = 1.9 and sd = 1.22
P(X < 3.25) = P(Z <(3.25 - 1.9)/1.22)
=P(Z< 1.106557)
= 0.8658
(b) 28 to 31 weeks
P (Z<?0.47)=0.3192
(c) 32 to 33 weeks
P (Z<?1.2)=0.1151
(d) 37 to 39 weeks
P (Z<?3.74)=0.0001
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