Question

The 10th percentile is inches.(Round to one decimal place as needed.)

Answer 1

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.

`x=z\sigma+\mu`
`\begin{gathered} x=(-1.282)(1.5in)+66in \\ x=-1.923+66 \\ x=64.077\approx64.1in \end{gathered}`

Answer:

The height at the 10th percentile is approximately 64.1 inches.

See the sketch of the normal curve below.