Question

birth weights of babies born to full - term pregnancies follow a normal distribution with a mean weight of 7 pounds with a standard deviation of 1.05 pounds. babies born with a weight in the top 3% are considered overweight. using standardized values, determine the minimum weight for a baby born to full - term pregnancy to be considered overweight.
6.45 pounds
8.97 pounds
5.03 pounds
7.55 pounds

Explanation:

Step1: Find the z - score

Since we want the top 3%, the area to the left of the z - score is \(1 - 0.03=0.97\). Looking up in the standard normal distribution table (or using a calculator with a normal - distribution function), the z - score \(z\) corresponding to an area of \(0.97\) is approximately \(z = 1.88\).

Step2: Use the z - score formula

The z - score formula is \(z=\frac{x-\mu}{\sigma}\), where \(\mu = 7\) (mean), \(\sigma=1.05\) (standard deviation), and \(z = 1.88\).
We solve for \(x\):

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Answer:

8.97 pounds