The masses of newborn children are normally distributed with a mean of 3.4 kg and a standard deviation of 0.8 kg. A newborn is at risk if the baby'd mass falls in the lowest 4%. These babies have a mass of less than ____?

To find the mass below which a newborn is considered at risk, we need to determine the z-score associated with the lowest 4% of values in a standard normal distribution.

Step 1: Convert the percentage to a z-score.
Since the distribution is normal, we can use the standard normal distribution table or a calculator to find the z-score corresponding to a cumulative probability of 0.04. The z-score associated with a cumulative probability of 0.04 is approximately -1.75.

Step 2: Use the z-score formula to find the raw score.
The z-score formula is given by z = (x - μ) / σ, where z is the z-score, x is the raw score, μ is the mean, and σ is the standard deviation.

Rearranging the formula to solve for the raw score, x:
x = (z * σ) + μ

Plugging in the values, we get:
x = (-1.75 * 0.8) + 3.4

Simplifying the equation:
x = -1.4 + 3.4
x = 2 kg

Therefore, a newborn is considered at risk if the baby's mass is less than 2 kg.