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 ____?
2.0 kg, which is 1.75 standard deviations below the mean.
Try using http://psych.colorado.edu/~mcclella/java/normal/accurateNormal.html
as a graphical aid
To find the mass at which a newborn is considered at risk (i.e., falling in the lowest 4%), we need to find the z-score corresponding to the 4th percentile and then convert it back to the corresponding mass using the mean and the standard deviation.
First, let's find the z-score for the 4th percentile. The z-score represents the number of standard deviations a value is from the mean in a normal distribution.
To find the z-score, we can use the standard normal distribution table or a statistical calculator. The z-score for the 4th percentile is approximately -1.75.
Now, we can convert the z-score back to the corresponding mass using the formula:
z = (x - mean) / standard deviation
Rearranging the formula to solve for x (mass), we have:
x = (z * standard deviation) + mean
Substituting the values we have:
x = (-1.75 * 0.8 kg) + 3.4 kg
Calculating the expression:
x = -1.4 kg + 3.4 kg
Therefore, the mass of a newborn baby considered at risk (falling in the lowest 4%) would be less than 2 kg.