Given:
mean = 66 inches
standard deviation (SD) = 1.5 inches
Find: height of the 10th percentile
Solution:
To determine the height of the 10th percentile, here are the steps:
1. Get the z-value of the given percentile. Find the z-value in the normal distribution table that has an area of 0.10 from the left of the normal curve.
Based on the standard normal distribution table, the z-value that covers 10% from the left of the normal curve is -1.282.
2. Use the formula below and plug into the formula the given values in the question and the identified z-value that is -1.282.
Answer:
The height at the 10th percentile is approximately 64.1 inches.
See the sketch of the normal curve below.