Question

Suppose that birth weights are normally distributed with a mean of 3466 grams and a standard deviation of 546 grams. Babies weighing less than 2500 grams at birth are considered "low weight." If we randomly select a baby, what is the probability that it has a low birth weight?

Answer 1

3.84% probability that it has a low birth weight

Explanation:

Problems of normally distributed samples are solved using the z-score formula.

In a set with mean
`\mu` and standard deviation
`\sigma`, the zscore of a measure X is given by:

`Z = (X - \mu)/(\sigma)`

The Z-score measures how many standard deviations the measure is from the mean. After finding the Z-score, we look at the z-score table and find the p-value associated with this z-score. This p-value is the probability that the value of the measure is smaller than X, that is, the percentile of X. Subtracting 1 by the pvalue, we get the probability that the value of the measure is greater than X.

In this problem, we have that:

`\mu = 3466, \sigma = 546`

If we randomly select a baby, what is the probability that it has a low birth weight?

This is the pvalue of Z when X = 2500. So

`Z = (X - \mu)/(\sigma)`

`Z = (2500 - 3466)/(546)`

`Z = -1.77`

`Z = -1.77` has a pvalue of 0.0384

3.84% probability that it has a low birth weight