104k views
0 votes
Newborn babies: A study conducted by the Center for Population Economics at the University of Chicago studied the birth weights of

690 babies born in New York. The mean weight was 3506 grams with a standard deviation of 840 grams. Assume that birth weight data are approximately bell-shaped. Estimate the number of newborns who weighed between 2666 grams and 4346 grams. Round to the nearest whole number.

User Delise
by
7.1k points

1 Answer

2 votes

Final answer:

To estimate the number of newborns who weighed between 2666 grams and 4346 grams, we can use the concept of z-scores. By calculating the z-scores for the lower and upper weights and finding the area under the bell-shaped curve between these two z-scores, we can estimate the proportion of newborns within this range. Multiplying this proportion by the total number of babies in the study gives us an estimate of the number of newborns.

Step-by-step explanation:

To estimate the number of newborns who weighed between 2666 grams and 4346 grams, we can use the concept of z-scores. A z-score measures how many standard deviations an observation is from the mean. First, let's calculate the z-scores for the lower and upper weights using the formula: z = (x - mean) / standard deviation. For the lower weight, z = (2666 - 3506) / 840 ≈ -0.1. For the upper weight, z = (4346 - 3506) / 840 ≈ 1.0.

Next, we can find the area under the bell-shaped curve between these two z-scores to estimate the proportion of newborns within this range. We can use a standard normal distribution table or a calculator to find these probabilities. The area between -0.1 and 1.0 is approximately 0.2787.

To estimate the number of newborns, we multiply this proportion by the total number of babies in the study: 0.2787 * 690 ≈ 192. Therefore, we can estimate that there were approximately 192 newborns who weighed between 2666 grams and 4346 grams.

User KingRichard
by
8.8k points