Question

In the United States, the mean birth weight for boys is 3.41 kg with a standard deviation of 0.55 kg. Assume that the distribution of birth weight is approximately normal. A baby is considered of low birth weight if it weighs less than 2.5 kg. What proportion of baby boys in the United States are born with low birth weight

Answer 1

Answer:

The proportion of baby boys in the United States that are born with low birth weight is 0.0495.

Step-by-step explanation:

Problems of normal distributions can be 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:

$Z = \frac{X - \mu}{\sigma}$

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.

3.41 kg with a standard deviation of 0.55 kg.

This means that $\mu = 3.41, \sigma = 0.55$

What proportion of baby boys in the United States are born with low birth weight?

This is the pvalue of Z when X = 2.5. So

$Z = \frac{X - \mu}{\sigma}$

$Z = \frac{2.5 - 3.41}{0.55}$

$Z = -1.65$

$Z = -1.65$ has a pvalue of 0.0495

The proportion of baby boys in the United States that are born with low birth weight is 0.0495.