Approximately what fraction of infants would you expect to have birth weights between 3210 g and 4430 g?

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 between 3210 g and 4430 g? (Express your answer as a decimal, not a percent, and round to three decimal places.)

Answer 1

Answer:

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.

Approximately what fraction of infants would you expect to have birth weights between 3210 g and 4430 g? (Express your answer as a decimal, not a percent, and round to three decimal places.)

Let us calculate the Z-scores:

Z (3210) = (3210 - 3432) / 482 = - 0.4606

Z (4430) = (4430 - 3432) / 482 = + 2.0705

Now, we have to find the area under the Standard Normal Distribution curve between these two Z values.

Area to left of the Standard Normal Curve when Z = - 0.4606 = 0.3228

Area to left of the Standard Normal Curve when Z = + 2.0705 = 0.9810

To get fraction of infants to have birth weights between 3210 g and 4430 g, we have to get the difference between the above 2 area values.

Answer:

Therefore, expected fraction of infants to have birth weights between 3210 g and 4430 g is:

= 0.9810 - 0.3228 = 0.658 (rounded to 3 decimal places)