Birth weights in the United States have a distribution that is approximately nor

Question

Birth weights in the United States have a distribution that is approximately normal with a mean of 3369g and a standard deviation of 567g (based on data from "Comparison of Birth Weight Distribution between Chinese and Caucasian Infants, " by Wen, Kramer, Usher, American Journal of Epidemiology, Vol.172, No.10). 1. One definition of a premature birth is that the birth weight is below 2500g. If a baby is randomly selected, find the probability of a birth weight below 2500g. 2. Another definition of a premature birth weight is in the bottom 10%. Find the birth weight that is the cutoff between the bottom 10% and the top 90% 3. A definition of a "very low birth weight" is one that is less than 1500g. If a baby is randomly selected, find the probability of a "very low birth weight." 4. If 25 babies are randomly selected, find the probability that their mean birth weight is grater that 3400g.

Explanation / Answer

Answer:

1).

Z value for 2500, z =(2500-3369)/567 =-1.53

P( x <2500) = P( z < -1.53)

=0.063

2).

Z value for bottom 10%= -1.282

Bottom x value = 3369-1.282*567 =2642.106

Cut off value =2642.106g

3).

Z value for 1500, z =(1500-3369)/567 =-3.30

P( x <1500) = P( z < -3.30)

=0.0005

4).

Standard error = 567/sqrt(25) =113.4

Z value for 3400, z =(3400-3369)/113.4 =0.27

P( mean x> 3400) = P( z > 0.27)

=0.3936

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