Approximately what fraction of infants would you expect to have birth weights above 4430 g? (Express your answer as a decimal, not a percent, and round to three decimal places.)

Question

Using all 1991 birth records in the computerized national birth certificate registry compiled by the National Center for Health Statistics (NCHS), statisticians Traci Clemons and Marcello Pagano found that the birth weights of babies in the United States are not symmetric ("Are babies normal?" The American Statistician, Nov 1999, 53:4). However, they also found that when infants born outside of the "typical" 37-43 weeks and infants born to mothers with a history of diabetes are excluded, the birth weights of the remaining infants do follow a Normal model with mean μ = 3432 g and standard deviation σ = 482 g. The following questions refer to infants born from 37 to 43 weeks whose mothers did not have a history of diabetes.

Approximately what fraction of infants would you expect to have birth weights above 4430 g? (Express your answer as a decimal, not a percent, and round to three decimal places.)

Answer 1

Hello Grace,

Since the infants born from 37 to 43 weeks whose mothers did not have a history of diabetes follow a normal distribution with mean 3432 g and standard deviation 482, we can find the proportion of infants with weights above 4430 g using a standard normal distribution and corresponding table of areas and z-scores (or an excel formula such as =1- NORM.DIST(4430,3432,482,TRUE) = 0.019201 ≈ 0.019)

First find the z-score using:

z = (x - μ) / σ = 2.07

Hence, P( X > 4430) = 1 - P(X < 4430) OR equivalently,

P(Z > 2.07) = 1 - P(Z < 2.07) = 1 - 0.9808 = 0.0192 ≈ 0.019

Notice how the excel result is more accurate than the table result, however results are the same when rounded to three decimal places.

I expect that you can substitute the necessary information to confirm that z = 2.07 and use the standard normal table to verify that the area to the left of 2.07 is indeed 0.9808. Furthermore, since the question is asking for fraction (or probability) of being greater than 4430 g the complement rule applies.

Hope this helps. Good Luck.