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Question

A study conducted by the Center for Population Economics at the University of Chicago studied the birth weights of 687 babies born in New York. The mean weight was 3008 grams with a standard deviation of 896 grams. Assume that birth weight data are approximately bell-shaped. Estimate the number of newborns who weighed between 1216 grams and 4800 grams. Round to the nearest whole number. The number of newborns who weighed between 1216 grams and 4800 grams is what?

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Answer to a math question A study conducted by the Center for Population Economics at the University of Chicago studied the birth weights of 687 babies born in New York. The mean weight was 3008 grams with a standard deviation of 896 grams. Assume that birth weight data are approximately bell-shaped. Estimate the number of newborns who weighed between 1216 grams and 4800 grams. Round to the nearest whole number. The number of newborns who weighed between 1216 grams and 4800 grams is what?

Expert avatar
Corbin
4.6
105 Answers
To estimate the number of newborns who weighed between 1216 grams and 4800 grams, we will use the concept of z-scores.

First, we need to calculate the z-score for each weight using the formula:

z = (x - ΞΌ) / Οƒ

where x is the weight, ΞΌ is the mean weight, and Οƒ is the standard deviation.

For the lower weight of 1216 grams:
z1 = (1216 - 3008) / 896

For the upper weight of 4800 grams:
z2 = (4800 - 3008) / 896

Next, we use a standard normal distribution table or calculator to find the area under the curve between these two z-scores. This area represents the proportion of newborns with weights between 1216 grams and 4800 grams.

Finally, to estimate the number of newborns in this weight range, we multiply the proportion by the total number of babies in the study.

Let's calculate the z-scores and find the proportion.

For the lower weight of 1216 grams:
z1 = (1216 - 3008) / 896 = -1.9911

For the upper weight of 4800 grams:
z2 = (4800 - 3008) / 896 = 2.0011

Using a standard normal distribution table or calculator, we find that the proportion of newborns with weights between z1 and z2 is approximately 0.9769.

Therefore, the estimated number of newborns who weighed between 1216 grams and 4800 grams is:

Estimated number = Proportion * Total number of babies
Estimated number = 0.9769 * 687

Now, rounding to the nearest whole number:

Estimated number β‰ˆ 671

Answer: The estimated number of newborns who weighed between 1216 grams and 4800 grams is approximately 671.

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