Question

in 2017, allegheny county reported 12,958 babies born.
a local pediatrician examined 288 babies and found that 24 had green eyes, 52 had hazel eyes, and 72 babies had blue eyes. based on the pediatricians sample, how many babies born in allegheny county would you expect to have green eyes?
remember:
use the pediatricians results to find the probability of a baby being born with green eyes using the formula
$p(event)=\frac{number\\ of\\ favorable\\ outcomes}{number\\ of\\ possible\\ outcomes}$.
use this probability to predict the number of babies born in allegheny county with green eyes.
a 1,080

Explanation:

Step1: Calculate the probability of green - eyed babies in the sample

The formula for probability is \(P(\text{event})=\frac{\text{number of favorable outcomes}}{\text{number of possible outcomes}}\).
Here, the number of favorable outcomes (green - eyed babies) is \(24\), and the number of possible outcomes (total babies in the sample) is \(288\).
So, \(P(\text{green eyes})=\frac{24}{288}=\frac{1}{12}\)

Step2: Predict the number of green - eyed babies in Allegheny County

We know that the total number of babies born in Allegheny County is \(N = 12958\).
Let \(x\) be the number of green - eyed babies. Using the probability formula \(P=\frac{x}{N}\), we can solve for \(x\).
Since \(P=\frac{1}{12}\) and \(N = 12958\), then \(x=P\times N\).
\(x=\frac{1}{12}\times12958\approx1080\) (rounded to the nearest whole number)

Answer:

A. 1,080