If the cranial capacities of an ancient population of humans from Indonesia are normally distributed with a mean of 1400cc and a standard deviation of 125cc. What is the cranial size of one of these ancient humans whose size is in the 67th percentile?

you can play around with Z table stuff here:

http://davidmlane.com/hyperstat/z_table.html

To find the cranial size of an ancient human in the 67th percentile, we can use the concept of z-scores and the standard normal distribution.

Step 1: Find the z-score corresponding to the 67th percentile.
The percentile corresponds to a specific z-score in the standard normal distribution. We can use a z-table or statistical software to find this value. In this case, the 67th percentile corresponds to a z-score of approximately 0.44.

Step 2: Use the z-score to find the cranial size.
The z-score formula is z = (X - μ) / σ, where X is the cranial size, μ is the mean cranial capacity, and σ is the standard deviation of cranial capacities.

Rearranging the formula, X = (z * σ) + μ

Plugging in the given values:
X = (0.44 * 125) + 1400

Calculating:
X = 55 + 1400
X = 1455

Therefore, the cranial size of an ancient human from Indonesia in the 67th percentile is approximately 1455cc.