Question

A study conducted by the Center for Population Economics at the University of Chicago studied the birth weight of 621 babies born in New York. The mean weight was 3234 grams with a standard deviation of 871 grams. Assume that birth weight data are approximately bell - shaped. Using the Empirical Rule, estimate the percentage of newborns whose weight was less than 2363 grams.

a)68%
b)95%
c)16%
d)84%

Answer 1

The estimated percentage of newborns whose weight was less than 2363 grams is 16%, following the Empirical Rule for a bell-shaped distribution where 16% of the data falls below one standard deviation from the mean.

Step-by-step explanation:

Using the Empirical Rule (also known as the 68-95-99.7 rule) for a bell-shaped distribution, we know that approximately 68% of the data falls within one standard deviation of the mean, 95% within two standard deviations, and 99.7% within three standard deviations.

To estimate the percentage of newborns whose weight was less than 2363 grams, we must find how many standard deviations below the mean this weight is:

Mean weight = 3234 grams
Standard deviation = 871 grams
Weight in question = 2363 grams

Z = (Weight in question - Mean weight) / Standard deviation
Z = (2363 - 3234) / 871
Z ≈ -1

A weight of 2363 grams is approximately one standard deviation below the mean. According to the Empirical Rule, approximately 16% of the data falls below one standard deviation from the mean. Therefore, the estimated percentage of newborns whose weight was less than 2363 grams is 16%.