Question

Explain How to Use the Empirical Rule to Solve a

Problem
In the United States, birth weights of newborn
babies are approximately normally distributed with
a mean of u = 3,500 g and a standard deviation of
o = 500 g
What percent of babies born in the United States
are classified as having a low birth weight < 2,500
g? Explain how you got your answer.
DONE

Answer 1

0.15%

Explanation:

The mean is μ = 3500 and the standard deviation is σ = 500.

2500 is 2 standard deviations below the mean, which we can calculate by finding the z-score.

z = (x − μ) / σ

z = (2500 − 3500) / 500

z = -2

According to the empirical rule, 99.7% of a normal distribution is between -2 and +2 standard deviations. Which means 0.3% is outside of that. Since a normal distribution is symmetrical, half of that, or 0.15%, is less than 2 standard deviations.