Question

A study conducted by the Center for Population Economics at the University of Chicago studied the birth weights of 614 babies born in New York. The mean weight was 3398 grams with a standard deviation of 892 grams. Assume that birth weight data are approximately bell-shaped. Estimate the number of newborns who weighed between 1614 grams and 5182 grams. Round to the nearest whole number.

Answer 1

The number of newborns who weighed between 1614 grams and 5182 grams was of 586.

Explanation:

Normal Probability Distribution

Problems of normal distributions can be solved using the z-score formula.

In a set with mean
`\mu` and standard deviation
`\sigma`, the z-score of a measure X is given by:

`Z = (X - \mu)/(\sigma)`

The Z-score measures how many standard deviations the measure is from the mean. After finding the Z-score, we look at the z-score table and find the p-value associated with this z-score. This p-value is the probability that the value of the measure is smaller than X, that is, the percentile of X. Subtracting 1 by the p-value, we get the probability that the value of the measure is greater than X.

The mean weight was 3398 grams with a standard deviation of 892 grams.

This means that
`\mu = 3398, \sigma = 892`

Proportion that weighed between 1614 and 5182 grams:

p-value of Z when X = 5182 subtracted by the p-value of Z when X = 1614.

X = 5182

`Z = (X - \mu)/(\sigma)`

`Z = (5182 - 3398)/(892)`

`Z = 2`

`Z = 2` has a p-value of 0.9772

X = 1614

`Z = (X - \mu)/(\sigma)`

`Z = (1614 - 3398)/(892)`

`Z = -2`

`Z = -2` has a p-value of 0.0228

0.9772 - 0.0228 = 0.9544.

Out of 614 babies:

0.9544*614 = 586

The number of newborns who weighed between 1614 grams and 5182 grams was of 586.