Question

The gestation period for human births can be taken as normally distributed with a mean of 266 days and a standard deviation of 16 days. If a gestation period is 276 days, what percentile among human births is this?

Answer 1

Answer:

74th percentile among human births.

Step-by-step 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:

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

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.

In this problem, we have that:

$\mu = 266, \sigma = 16$

If a gestation period is 276 days, what percentile among human births is this?

This is the pvalue of Z when X = 276. So

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

$Z = \frac{276 - 266}{16}$

$Z = 0.63$

$Z = 0.63$ has a pvalue close to 0.74.

So this is the 74th percentile among human births.